Strategic competition - Forsiden · Tore Nilssen – Strategic Competition – Theme 1 – Slide 4 Even in the study of a single industry, it may be helpful to have different models

Tore Nilssen – Strategic Competition – Theme 1 – Slide 1

Strategic competition American term: Industrial organization A better name: The economics of industry

- the study of activities within an industry, mainly with respect to competition among the firms in a product market.

Why is this topic important? The model of perfect competition is unrealistic.

- Who set the prices? – The firms.

- Can they influence the price? – Yes, for example if their products differ, or if they are few.

But: difficult to find a general model of imperfect competition. Many models with varying applications

- Is it smart to have a whole battery of models?

The predictions from the perfect-competition model do

not fit. In many industries: - high profits - p > MC

Competition policy


The study of an industry - few firms - partial equilibrium - how do the firms compete with each other?

- setting prices? quantities? - making investments? advertising? R&D?

capacity? - location of outlets

- what do they do to avoid competition?

- product differentiation - entry deterrence - predatory actions - collusion - merger

Various models, all with the same analytical tool: game theory


What is the right model to use? - What kind of market are we looking at?

Example: market for petrol vs. market for cars petrol: homogeneous good car: heterogeneous good petrol: easy for firms to supervise each other’s prices car: price supervision difficult Product differentiation weaker competition petrol market more competitive Price supervision: easy to coordinate on prices petrol market less competitive Both markets may have the same mark-up, but explanations may differ. In order to understand how firms in an industry compete (or not), we need a catalogue of different models.


Even in the study of a single industry, it may be helpful to have different models of strategic competition in mind. Example: Norwegian airlines.

(source: Norwegian Competition Authority)

Predation Entry deterrence Non-price competition Collusion Merger Consumer switching costs


Central concepts from game theory Extensive form vs. normal form Strategy vs. action Pure strategy vs. mixed strategy Dominated strategy Nash equilibrium Subgame-perfect equilibrium Repeated games Repetition of game theory: Tirole, secs 11.1-11.3 (for ch 9: secs 11.4-11.5) Exercises 11.1, 11.4, 11.9.


Competition in the short run or: Static oligopoly theory Firms make decisions simultaneously Actions chosen from continuous action spaces Differentiable profit functions First-order conditions Nash equilibrium with 2 firms:

0, *

2*1

i

i

s

ss i = 1, 2

Each firm’s decision is optimum, given the other firm’s equilibrium decision. The other firm’s decision is exogenous. Thus, we can find one firm’s optimum decision given the other firm’s choice: Best-response functions R1(s2) is firm 1’s best-response function, defined by:

0

,

1

2211

s

ssR


Best-response curves: The slope of the best-response curve:

02

21

12

121

12

ds

ssdR

s

21

1221

12

2

121

'

s

ss

ds

dRsR

Second-order condition 021

12

s

Therefore: sign R1’(s2) = sign 21

12

ss

s2*

R2(s1)

R1(s2)

s1

s2

s1*


021

12

ss

:

An increase in s2 implies a reduction in firm 1’s payoff from a marginal increase in s1. This implies a reduction in firm 1’s optimum. The two firms’ choice variables are strategic substitutes.

021

12

ss

:

An increase in s2 implies an increase in firm 1’s payoff from a marginal increase in s1. This implies an increase in firm 1’s optimum. The two firms’ choice variables are strategic complements. Generally, but not always: prices are strategic complements quantities are strategic substitutes


Price competition A firm’s price is a short-term commitment. So a regular picture of competition in the short run is one of competition in prices. Modelling is a trade-off between making a model

- simple, so that we can understand it; and

- reasonable, so that we can use it. Let us start out with simplicity. Two firms, homogeneous goods (perfect substitutes). Consumers care only about price. Market demand: D(p), D’ < 0. Constant unit cost: c. No capacity constraints. Firms choose prices simultaneously and independently. Equilibrium prices – Bertrand equilibrium. (Joseph Bertrand, 1883) Firm 1’s profit: 1(p1, p2) = (p1 – c)D1(p1, p2), where

21

2112

1

211

211

if ,0

if,

if ,

,

pp

pppD

pppD

ppD


1(p1, p2) is discontinuous, because D1(p1, p2) is. First-order approach not applicable. Nash equilibrium: 1(p1*, p2*) 1(p1, p2*), p1. 2(p1*, p2*) 2(p1*, p2), p2. Result: There exists a unique equilibrium, in which p1* = p2* = c Two steps in the proof. Step 1: This is an equilibrium. Step 2: No other price combination is an equilibrium. [Exercise 5.1: cost asymmetry]

p1

p2

(i)

(ii)

(iv)

(iii)

c


The same result holds for any number of firms 2. So there is nothing between monopoly and perfect competition (the Chicago school). Or is there? The model lacks realism.

Resolving the Bertrand paradox (i) Product differentiation Consumers care for both price and product characteristics. No longer true that R(c) = c. If p2 = c, then p1 = c + provides firm 1 with positive profit. Thus, p = c no longer equilibrium. [Theme 3] (ii) Time horizon Consider the case p1 = p2 > c. Not an equilibrium, because firm 1 is better off with reducing its price strictly below p2. But what if firm 2 can respond to this? Would it set a price even lower? If so, could it be that firm 1 does not have incentives for a price reduction to start with? [Theme 2]


(iii) Capacity constraints Firms cannot sell more than they are able to produce. Capacity constraints: 1q and 2q . Suppose 1q < D(c). p = c is no longer equilibrium Suppose firm 1’s price is p1 = c. If now firm 2 sets p2 = c + , then firm 1 faces a higher demand than its capacity. Some consumers will have to go to the high-price firm 2, who therefore earns a profit. Capacity constraints are an extreme version of decreasing returns to scale. [Next slides]


Price competition with capacity constraints Consumers are rationed at the low-price firm. But who are the rationed ones? As before: two firms; homogeneous goods.

Efficient rationing If p1 < p2 and 1q < D(p1), then the residual demand facing firm 2 is:

otherwise ,0

,if,~ 121222

qpDqpDpD

This is the rationing that maximizes consumer surplus: The consumers with the highest willingness to pay get the low price.

D(p)

q2

p2

p1

1

q


Proportional rationing Let p1 < p2 and 1q < D(p1). Instead of favouring the consumers with the highest willingness to pay, all consumers have the same chance of getting the low price. Probability of being supplied by the low-price firm 1 is:

1

1

pD

q

The residual demand facing the high-price firm 2 is:

1

1222 1

~

pD

qpDpD

Not efficient – some consumers get supplies despite having a willingness to pay below p2, consumers’ marginal cost.

q2

D(p) p2

p1

1

q


Example Two firms, homogeneous demand: D(p) = 1 – p Zero marginal costs of production: c = 0. High investment costs have led to low capacity:

3

121 qq .

Assume efficient rationing. Define: p* = 1 – 21 qq . [Note: p* ≥

3

1 > c.]

Is p1 = p2 = p* an equilibrium? Note that D(p*) = 21 qq ; total capacity exactly covers demand at this price. Can another price be preferable for firm 1 to p*, if firm 2 sets p2 = p*? (i) Consider p1 < p2 = p*. A lower price for firm 1

without any increase in sales. (ii) Consider p1 > p2 = p*. Firm 1’s sales less than

before: q1 = 11

~pD = D(p1) – 2q = 1 – p1 – 2q

p1 = 1 – q1 – 2q


Profit of firm 1: 1 = p1 11

~pD

Equivalently: 1 = (1 – q1 – 2q )q1 Is it profitable for firm 1 with a price above p*? Equivalently: Is it profitable with a quantity below 1q ?

211

1 21 qqdq

d

Second-order condition: 21

12

dq

d < 0.

021| 211

111

qqdq

dqq

Optimum is at 1q . Thus, the optimum price for firm 1 is p*. Equivalently for firm 2. Thus, p1 = p2 = p* in equilibrium. Is this equilibrium unique? Yes. Larger capacities: No equilibria in pure strategies. [Exercise 5.2]


Capacity a more long-term decision than price Consider the following two-stage game: Stage 1: Firms choose capacities Stage 2: Firms choose prices Investment costs: c0 per unit of capacity Suppose c0 is so high that, in equilibrium, capacities will be low. We can then make use of our analysis of the price game: Prices equal p*. Profit net of investment costs: 1( 1q , 2q ) = {[1 – ( 1q + 2q )] – c0} 1q . Now, the game is equivalent to a one-stage game in capacities where demand = total capacity = total supply. That is, a one-stage game in quantities. (Augustin Cournot, 1838) With efficient rationing and a concave demand function, the two games are equivalent in equilibrium outcome, for all c0. Therefore, a model of one-stage quantity competition, with prices coming from nowhere, can be understood as a simple substitute for a more realistic but more complex model where firms compete in capacities and thereafter in prices.


The Cournot model Two firms choose quantities simultaneously. Costs: Ci(qi) Total production: Q = q1 + q2

Inverse demand: P(Q), P’ < 0. Profit, firm 1: 1(q1, q2) = q1P(q1 + q2) – C1(q1). First-order condition:

1

1

q = P(q1 + q2) + q1P’(q1 + q2) – C1’(q1) = 0

q1P’(q1 + q2) – the infra-marginal effect of an

increase in quantity

Equilibrium: 1

1

q = 0;

2

2

q = 0.


For firm 1:

P – C1’ = – q1P’ =

QP

Q

q

QPQ

q1

'

1

11 '

Q

P

P

Q

q

P

CP

'

1

11'

L1 = P

CP '1 – the Lerner index of firm 1

1 = Q

q1 – firm 1’s market share

D(p) – the market demand

D(P(Q)) Q

D’(p) P’(Q) = 1 Demand elasticity:

Q

P

PD

PD'

1'

L1 = 1

Note: (i) 1/ > 0 L1 > 0 P > C1’. (ii) Monopoly: 1 = 1, and L1 = 1/.


n firms: n

i iqQ1

i(q1, …, qn) = qiP(Q) – Ci(qi)

0''

1

ii

ii

i

Cdq

dQPqQP

q

Example: P(Q) = a – Q;

Ci(qi) = C(qi) = cqi, where a > c. First-order condition firm i: a – Q – qi – c = 0. All firms identical q1 = … = qn = q, Q = nq Applied to the first-order condition: a – nq – q – c = 0

1

n

caq

P = a – nq = cn

cacn

nca

n

cana

111

Q = nq = can

n 1

= 2

111

n

caq

n

cacqn

cacq

n P c, Q a – c, 0. [Exercises 5.3, 5.4, 5.5]


Bertrand vs. Cournot Competing models? – No. Firms set prices. When capacity constraints are of little importance, the Bertrand model is the preferred one. When capacity constraints are present to an important extent (decreasing returns to scale), the Cournot model is the best choice. Measuring concentration A substitute for measuring price-cost margins, since costs are unobservable. A popular measure: the Herfindahl index. n

i iHR1

2

Model: n firms, Ci(qi) = ciqi, quantity competition Total industry profits:

i Hi iiii

ii ii RD

DPQqPqcP

'

22

Assume: = 1 pD(p) = k D(p) = k/p D2/(– D’) = k Hi i Rk

The Herfindahl index is proportional to total industry profits. [Exercises 5.6, 5.7]


Dynamic oligopoly theory

• Dynamic price competition • Collusion

Collusion – price coordination Illegal in most countries

- Explicit collusion not feasible - Legal exemptions

Recent EU cases

• Banking – approx. 1.7 billion Euros in fines (2013) • Cathodic ray tubes – 1.5 billion Euros (2012) • Gas – approx. 1.1 billion Euros in fines (2009) • Car glass – approx. 1.4 billion Euros (2008)

Website: ec.europa.eu/competition/cartels/cases/cases.html Puerto Rico, US, 2013: 5-year sentence for price-fixing


Tacit collusion

Hard to detect – not many cases. Repeated interaction Theory of repeated games Deviation from an agreement to set high prices has

- a short-term gain: increased profit today - a long-term loss: deviation by the others later on

Tacit collusion occurs when long-term loss > short-term gain Model Two firms, homogeneous good, C(q) = cq Prices in period t: (p1t, p2t) Profits in period t: π1(p1t, p2t), π2(p1t, p2t) History at time t: Ht = (p10, p20, …, p1, t – 1, p2, t – 1) A firm’s strategy is a rule that assigns a price to every possible history.


A subgame-perfect equilibrium is a pair of strategies that are in equilibrium after every possible history: Given one firm’s strategy, for each possible history, the other firm’s strategy maximizes the net present value of profits from then on. T – number of periods T finite: a unique equilibrium period T: p1T = p2T = c, irrespective of HT. period T – 1: the same and so on T infinite (or indefinite) At period τ, firm i maximizes

( )∑∞

=

−

τ

τπδt

ttit pp 21 , ,

r+=

11δ

The best response to (c, …) is (c, …). But do we have other equilibria? Can p > c be sustained in equilibrium?


Trigger strategies: If a firm deviates in period t, then both firms set p = c from period t + 1 until infinity. [Optimal punishment schemes? Renegotiation-proofness?] Monopoly price: pm = arg max (p – c)D(p) Monopoly profit: πm = (pm – c)D(pm) A trigger strategy for firm 1: • Set p10 = pm in period 0 • In the periods thereafter,

� p1t(Ht) = pm, if Ht = (pm, pm, …, pm, pm) � p1t(Ht) = c, otherwise

If a firm collaborates, it sets p = pm and earns πm/2 in every period. The optimum deviation: pm – ε, yielding ≈ πm for one period. An equilibrium in trigger strategies exists if:

2

mπ(1 + δ + δ2 + … ) ≥ πm + 0 + 0 + …

⇔ δ−1

121

≥ 1 ⇔ δ ≥ 21


The same argument applies to collusion on any price p ∈ (c, pm]. ⇒ Infinitely many equilibria. The Folk Theorem. Collusion when demand varies Demand stochastic. Periodic demand is

low: D1(p) with probability ½ high: D2(p) with probability ½ D1(p) < D2(p), ∀ p.

The demand shocks are i.i.d. Each firm sets its price after having observed demand. What are the best collusive strategies for the two firms? Trigger strategies: A deviation is followed by p = c forever.

π2

π1


What are the best collusive prices? One price in low-demand periods and one in high-demand periods: p1 and p2. πs(p) – total industry profit in state s when both firms set p. With prices p1 and p2 in the two states, each firm’s expected net present value is:

( )( ) ( )( )∑∞=

−+−= 0 222

111

221

221

tt cp

pDcp

pDV δ

= ( )δ−141 [D1(p1)(p1 – c) + D2(p2)(p2 – c)]

= ( ) ( )

( )δππ

−+

142211 pp

The best possible collusive price in state s is:

psm = arg max (p – c)Ds(p), s = 1, 2.

πs

m = (psm – c)Ds(ps

m), s = 1, 2. If the firms can collude on these prices, then:

( )1 2

4 1

m m

Vπ π

δ+=−


A deviation in state s receives a gain equal to: πsm

For (p1m, p2

m) to be equilibrium prices, we must have: πs

m ≤ ½πsm + δV ⇔ πs

m ≤ 2δV The difficulty is state 2 (high-demand), since π1

m < π2m.

The equilibrium condition becomes:

( )1 2

2 24 1

m mm π ππ δ

δ+≤−

⇔ 0

2

13

2 δδ

ππ

≡+

≥

m

m

0 < m

m

2

1

ππ

< 1 ⇒ 2

1 < δ0 < 3

2

But what if δ ∈ [

2

1 , δ0)? Can we still find prices at which

the firms can collude?


The problem is again state 2. We need to set p2 so that

( ) ( )( )

1 2 22 2 2

4 1

m pp

π ππ δ

δ+

≤−

⇒ ( ) mp 122 32π

δδπ−

=

2

1 ≤ δ < 3

2 ⇒ δ

δ32−

≥ 1 ⇒ π2 ≥ π1

So: prices below monopoly price in high-demand state – during boom. Could even be that p2 < p1. But is this a price war? More realistic demand conditions: Autocorrelation – business cycle. Collusion most difficult to sustain just as the downturn starts. Haltiwanger & Harrington, RAND J Econ 1991 Kandori, Rev Econ Stud 1991 Bagwell & Staiger, RAND J Econ 1997

[Exercise 6.4]


Empirical studies of collusion • the railroad cartel

- Porter Bell J Econ 1983 - Ellison RAND J Econ 1994

• collusion among petrol stations

- Slade Rev Econ Stud 1992 • collusion in the soft-drink market: prices and advertising

- Gasmi, et al., J Econ & Manag Strat 1992 • collusion in procurement auctions

- Porter & Zona J Pol Econ 1993 (road construction) - Pesendorfer Rev Econ Stud 2000 (school milk)

Infrequent interaction Suppose the period length doubles.

δ → δ2 Collusion feasible if:

δ2 ≥ 21

⇔ 2

1≥δ ≈ 0.71


Multimarket contact Market A: Frequent interaction, period length 1. Collusion if δ ≥ ½. Market B: Infrequent interaction, period length 2. Collusion if δ2 ≥ ½. (How could frequency vary across markets?) What if both firms operate in both markets? Can the firms obtain collusion in both markets even in cases where δ2 < ½ < δ? A deviation is most profitable when both markets are open. Deviation yields: 2πm Collusion yields: [πm/2] every period, plus [πm/2] every second period (starting today) Collusion can be sustained if:

2

mπ[1 + δ + δ2 + … ] +

2

mπ[1 + δ2 + δ4 + … ] ≥ 2πm

⇔ 21

121

11

21

2 ≥−

+− δδ

⇔ 4δ2 + δ – 2 ≥ 0 ⇔ 8

133−≥δ ≈ 0.59


Secret price cuts, or: Price coordination when supervising the partners is difficult

Own demand observable Market demand not observable Other firms’ prices not observable When own demand is low, is it because market demand is low, or because partners default? Punishment (p = c) is necessary. But punishment forever? Can firms coordinate prices without being able to observe each other’s prices? Punishment starts when one observes low demand. Punishment phase lasts for a finite number of periods. Even colluding firms have periods of ‘‘price wars”. Model: Two firms; homogeneous products; MC = c. In each period: firms set prices; consumers choose the firm with the lower price. Market demand is either: D = 0, with probability α; D = D(p), with probability (1 – α).


Both firms know it if at least one firm has zero profit in a period. Either:

- market demand is zero and both firms have zero profit, or

- one firm has cut its price and knows that the other firm has zero profit

Strategy: • Start with p = pm. • Set p = pm until (at least) one firm has zero profit. • If this happens, then set p = c for T periods. • After T periods, return to p = pm until (at least) one firm

has zero profit.

And so on. Is there an equilibrium in which each firm plays this strategy? T must be determined.


Two phases: • Colluding phase • Punishment phase

V+ = net present value of a firm in the colluding phase V− = net present value of a firm at the start of the punishment phase

( ) −++ +

+−= VVV

m

αδδπα2

1

V− = δTV+ Equilibrium condition: V+ ≥ (1 − α)(πm + δV−) + αδV− = (1 − α)πm + δV−

( ) ( ) −−+ +−≥+

+−⇔ VVV m

m

δπααδδπα 12

1

( )2

m

VVπδ ≥−⇔ −+

( )2

1m

TVπδδ ≥−⇔ +


( ) ++++ +

+−= VVV T

m1

21 αδδπα

( )( ) 111

21

++

−−−

−= T

m

Vαδδα

πα

( )( ) ( )

21

112

1

1

mT

T

m

πδδαδδα

πα≥−

−−−

−+

2δ(1 − α) + (2α − 1)δT + 1 ≥ 1 The best equilibrium has the highest possible V+. The firms’ problem: maxT V

+, such that: 2δ(1 − α) + (2α − 1)δT + 1 ≥ 1 But: dV+/dT < 0. So we restate the problem. min T, such that: 2δ(1 − α) + (2α − 1)δT + 1 ≥ 1


T = 0 is too low – there has to be some punishment, even under collusion: 2δ(1 − α) + (2α − 1)δ = δ < 1 And the lefthand side must be increasing in T:

( ) ( )[ ]11212 +−+− T

dT

d δααδ

( )� 2

10ln12

0

1 <⇔>−=<

+ αδδα T

If α ≥ ½, then collusion is impossible: The probability of zero market demand is too large. If α < ½, then 2α − 1 < 0. But (2α − 1)δT + 1 → 0 as T → ∞.

Equilibrium condition satisfied for some T if also 2δ(1 − α) ≥ 1

All in all: Collusion can occur in equilibrium if:

• α < ½

• α

δ−

≥1

121

T is chosen as the lowest integer that satisfies:

2δ(1 − α) + (2α − 1)δT + 1 ≥ 1 Example: δ = ¾, α = ¼. Condition: (¾)T + 1 ≤ ¼ ⇒ T* = 4. But often T* is smaller: δ = 0.9, α = 0.2 ⇒ T* = 2.


Price rigidities • Menu costs • Price reactions not punishments, but attempts to regain

market share Suppose

- a price is fixed for two periods - firms alternate at setting price

Duopoly with alternating price setting • A discrete price grid • Markov strategies: strategies based only on directly

payoff-relevant information Example: A trigger strategy is not Markov; no price from the past has a direct effect on a firm’s profit today, only an indirect effect, because other firms use trigger strategies. A restriction to Markov strategies would be too strong when moves are simultaneous. Here, moves are alternating. Model: duopoly; each firm’s price fixed for two periods; firm 1 sets price in odd-numbered periods (1 – 3 – 5 – …), firm 2 in even-numbered periods (2 – 4 – 6 – …).


Markov reaction functions: Let pit be the price set by firm i in period t. Firm 1’s reaction function:

p1, 2k + 1 = R1(p2, 2k), k = 0, 1, 2, … Firm 2’s reaction function:

p2, 2k + 2 = R2(p1, 2k + 1), k = 0, 1, 2, …

Markov perfect equilibrium: An equilibrium in Markov reaction functions. At the start of each subgame, the firm that makes the move chooses an optimum strategy, given the restriction only to pay attention to payoff-relevant information, and given the other firm’s equilibrium strategy. The two firms at any point in time:

‘‘the active” and ‘‘the other” Consider the active firm’s decision today. Suppose the other firm set the price ph last period; this is also its price today. – We are in state h. Vh – the active firm’s net present value in state h. Wh – the other firm’s net present value in state h. Tomorrow, the roles are changed.


Profit per period: π(own price, the other’s price) ⇒ ( )[ ]khk

kh WppV δπ += ,max

A symmetric equilibrium: R1(⋅) = R2(⋅) = R(⋅) Mixed strategy: A firm may be indifferent between one or more prices, and in equilibrium, the other firm has beliefs about which of these prices will be chosen. These beliefs will then constitute the firm’s mixed strategy. αhk – the probability (according to the other firm’s beliefs) that a firm in state h chooses price pk.

Note: 1=∑k

hkα

A symmetric equilibrium can be described by a transition matrix: Suppose there are H possible prices.

��

1

111

state to

......

..

..

..

......

state from

k

h

HHH

H

αα

αα

= A


Equilibrium conditions

( )[ ]∑ +=k

khkhkh WppV δπα ,

( )[ ]∑ +=l

llkklk VppW δπα ,

These are the values of Vh and Wk that follow from the transition matrix A.

[Vh – π(pk, ph) – δWk]αhk = 0, ∀ h, k. Vh ≥ π(pk, ph) + δWk, ∀ h, k.

Complementary slackness: If αhk > 0, it must be because Vh = π(pk, pl) + δWk, that is, because pk maximizes the firm’s net present value in state h.

1=∑

khkα , ∀ h

αhk ≥ 0, ∀ h, k.


Example: D(p) = 1 – p; c = 0 The price grid: ph =

6

h , h = 0, …, 6.

Competitive price: p0 = 0. Monopoly price: pm = p3 = ½. Two (symmetric Markov perfect) equilibria (at least):

1. ‘‘Kinked demand curve”: The other firm does not follow you if you increase the price but undercuts you if you decrease the price.

R(1) = R(6

5 ) = R(3

2 ) = R(2

1 ) = R(0) = 2

1 ;

R(3

1 ) = 6

1 ; R(6

1 ) ∈ {6

1 , 2

1 }.

• Either the game starts in state 3 and stays there, or it

ends there sooner or later (absorbing state).

• A mixed strategy in state 1 – a waiting game (‘‘war of attrition”): Each firm is indifferent between meeting p1 with p1, and making a short-term sacrifice in order to get the monopoly price from next period on.

• The equilibrium is sustainable only if each firm is able

to supply the whole market demand at p1 = 6

1 : D(6

1 ) =

6

5 . In the absorbing state 3, each firm sells 2

1 D(p3) = 4

1

but needs to keep an excess capacity of 6

5 – 4

1 = 12

7 .


2. Price war: The firms undercut each other.

R(1) = R(6

5 ) = 3

2 ; R(3

2 ) = 2

1 ; R(2

1 ) = 3

1 ;

R(3

1 ) = 6

1 ; R(6

1 ) = 0; R(0) ∈ {0, 6

5 }.

• Unstable prices: no absorbing state.

• Edgeworth cycle.

• Again a waiting game. But now the price jumps

beyond the monopoly price. • Multiple equilibria, even when we restrict attention to

Markov strategies. • Fewer equilibria than in an ordinary repeated game. • p = c is no longer an equilibrium; there is always some

price collusion in equilibrium. Other cases of dynamic price competition • Brand loyalty / consumer switching costs

• Durable goods


Product differentiation How far does a market extend? Which firms compete with each other? What is an industry? Products are not homogeneous. Exceptions: petrol, electricity. But some products are more equal to each other than to other products in the economy. These products constitute an industry. A market with product differentiation. But: where do we draw the line? Example:

- beer vs. soda? - soda vs. milk? - beer vs. milk?


Two kinds of product differentiation (i) Horizontal differentiation: Consumers differ in their

preferences over the product’s characteristics. Examples: colour, taste, location of outlet.

(ii) Vertical differentiation: Products differ in some

characteristic in which all consumers agree what is best. Call this characteristic quality. (quality competition)

Horizontal differentiation Two questions: 1. Is the product variation too large in equilibrium? 2. Are there too many variants in equilibrium? Question 1: A fixed number of firms. Which product variants will they choose? Question 2: Variation is maximal. How many firms will enter the market? The two questions call for different models.


Variation in equilibrium Will products supplied in an unregulated market be too similar or too different, relative to social optimum? Hotelling (1929) Product space: the line segment [0, 1]. Two firms: one at 0, one at 1. Consumers are uniformly distributed along [0, 1]. A consumer at x prefers product variant x. Consumers have unit demand: p s 1 q

x 0 1


Disutility from consuming product variant y: t(|y – x|) – ‘‘transportation costs”

Linear transportation costs: t(d) = td Generalised prices (with firm 1 at 0 and firm 2 at 1):

p1 + tx and p2 + t(1 – x) The indifferent consumer: xɶ s – p1 – t xɶ = s – p2 – t(1 – xɶ ).

( ) 2 11 2

1,

2 2

p px p p

t

−⇒ = +ɶ

[But check that: (i) 0 ≤ xɶ ≤ 1; (ii) xɶ wants to buy.]

x

s – p1– tx

s – p2 – t(1 – x)

( )1 2,x p pɶ


Normalizing the number of consumers: N = 1 (thousand)

D1(p1, p2) = xɶ = t

pp

221 12 −+

D2(p1, p2) = 1 – xɶ = t

pp

221 21 −+

Constant unit cost of production: c

( ) ( )

−+−=t

ppcppp

221

, 121211π

Price competition.

Equilibrium conditions: 01

1 =∂∂

p

π; 0

2

2 =∂∂

p

π

FOC[1]:

( )��

soldunit per gain increasesprice increased

12

sales reducesprice increased

1 221

21

t

pp

tcp

−++

−− = 0

⇒ FOC[1]: 2p1 – p2 = c + t FOC[2]: 2p2 – p1 = c + t ⇒ p1* = p2* = c + t


• The indifferent consumer does want to buy if:

tcs2

3+≥

• Prices are strategic complements:

021

21

12

>=∂∂

∂tpp

π

Best-response function: p1 = ½(p2 + c + t) The degree of product differentiation: t Product differentiation makes firms less aggressive in their pricing.


But are 0 and 1 the firms’ equilibrium product variants? Two-stage game of product differentiation: Stage 1: Firms choose locations on [0, 1]. Stage 2: Firms choose prices. Linear vs. convex transportation costs.

• Convex transportation costs analytically tractable – but economically less meaningful?

Assume quadratic transportation costs. Stage 2: Firms 1 and 2 located at a and 1 – b, a ≥ 0, b ≥ 0, a + b ≤ 1. The indifferent consumer: p1 + t(xɶ – a)2 = p2 + t(1 – b – xɶ )2

( ) ( )2 11

12 2 1

p px a a b

t a b

−= + − − +− −

ɶ

D1(p1, p2) = xɶ , D2(p1, p2) = 1 – xɶ

( ) ( ) ( ) ( )

−−−+−−+−=

bat

ppbaacppp

121

21

, 121211π


Equilibrium conditions: 01

1 =∂∂

p

π; 0

2

2 =∂∂

p

π

FOC[1]: 2p1 – p2 = c + t(1 – a – b)(1 + a – b)

FOC[2]: 2p2 – p1 = c + t(1 – a – b)(1 – a + b) Equilibrium:

( )

−+−−+=3

111ba

batcp

( )

−+−−+=3

112ab

batcp

• Symmetric location: a = b ⇒ p1 = p2 = c + t(1 – 2a) • A firm’s price decreases when the other firm gets closer:

01 <db

dp .

• Stage-2 outcome depends on locations:

p1 = p1(a, b), p2 = p2(a, b) Stage 1: π1(a, b) = [p1(a, b) – c]D1(a, b, p1(a, b), p2(a, b))


( )

∂∂

∂∂+

∂∂

∂∂+

∂∂−+

∂∂=

a

p

p

D

a

p

p

D

a

Dcp

a

pD

da

d 2

2

11

1

111

11

1π

( ) ( )

∂∂

∂∂+

∂∂−+

∂∂

∂∂−+=

=

a

p

p

D

a

Dcp

a

p

p

DcpD 2

2

111

1

0

1

111

��

( )�

��

)(

0 effect;

strategic

0

2

0

2

1

0 effect;direct

11

1

��

<

<>

>

∂∂

∂∂+

∂∂−=

a

p

p

D

a

Dcp

da

dπ

Moving toward the middle: A positive direct effect vs. a negative strategic effect.

( ) ( )

( ) 21

if ,016

53

1321

1221

2121

≤>−−−−=

−−−+=

−−−+=

∂∂

aba

ba

ba

ab

bat

pp

a

D

( )2322 −=

∂∂

ata

p < 0

( )batp

D

−−=

∂∂

12

1

2

1 > 0

( ) ( ) ( ) 016

13

13

2

16

532

2

11 <−−++−=

−−−+

−−−−=

∂∂

∂∂+

∂∂

ba

ba

ba

a

ba

ba

a

p

p

D

a

D

Equilibrium: a* = b* = 0.


Strategic effect stronger than direct effect. Maximum differentiation in equilibrium. Social optimum: No quantity effect. Social planner wants to minimize total transportation costs. (Kaldor-Hicks vs. Pareto) In social optimum, the two firms split the market and locate in the middle of each segment: ¼ and ¾. In equilibrium, product variants are too different. • Crucial assumption: convex transportation costs. • Also other equilibria, but they are in mixed strategies.

[Bester et al., ‘‘A Noncooperative Analysis of Hotelling’s Location Game”, Games and Economic Behavior 1996]

• Multiple dimensions of variants: Hotelling was almost

right [Irmen and Thisse, ”Competition in multi-characteristics spaces: Hotelling was almost right”, Journal of Economic Theory 1998]

• Head-to-head competition in shopping malls: Consumers’ shopping costs.

[Klemperer, “Equilibrium Product Lines”, AER 1992]

Have we really solved the problem whether or not the equilibrium provision of product variants has too much or too little differentiation?


Too many variants in equilibrium? A model without location choice. Focus on firms’ entry into the market. The circular city Circumference: 1 Consumers uniformly distributed around the circle. Number of consumers: 1 Linear transportation costs: t(d) = td Unit demand, gross utility = s Entry cost: f Unit cost of production: c Profit of firm i: πi = (pi – c)Di – f, if it enters, 0, otherwise


Two-stage game. Stage 1: Firms decide whether or not to enter. Assume entering firms spread evenly around the circle.

Stage 2: Firms set prices. If n firms enter at stage 1, then they locate a distance 1/n apart. Stage 2: Focus on symmetric equilibrium. If all other firms set price p, what then should firm i do? Each firm competes directly only with two other firms: its neighbours on the circle. At a distance x~ in each direction is an indifferent consumer:

−+=+ xn

tpxtpi~1~

−+= ipn

tp

tx

21~

Demand facing firm i:

Di(pi, p) = 2x~ = t

pp

ni−+1


Firm i’s problem:

( ) ft

pp

ncp i

iipi

−

−+−= 1maxπ

( ) 011 =−−

−+=∂∂

tcp

t

pp

np ii

i

iπ

n

tcppi +=−2

In a symmetric equilibrium, all prices are equal. ⇒ pi = p.

n

tcp +=

Stage 1: How many firms will enter?

Di = n

1

( ) fn

tf

ncpi −=−−= 2

1π

π = 0 ⇒ f

tn =

⇒ p = c + ft

t = c + tf


Condition: Indifferent consumer wants to buy:

n

tps

2+≥ = c + tf

23

⇔ ( )2

94

cst

f −≤

Exercise 7.3: What if transportation costs are quadratic? [Exercise 7.4: What if fixed costs are large?] Social optimum: Balancing transportation and entry costs.

Average transportation cost: t ( x~21

) = n

t

21

2=

n

t

4

The social planner’s problem:

+n

tnf

n 4min

FOC: 04 2 =−n

tf ⇒ n* =

f

t

21

< ne

Too many firms in equilibrium. Private motivation for entry: business stealing Social motivation for entry: saving transportation costs [Exercise: What happens with ne/n* as N (number of consumers) grows?]


Advertising • informative • persuasive Persuasive: shifting consumers’ preferences? Focus on informative advertising. Hotelling model, two firms fixed at 0 and 1, consumers uniformly distributed across [0,1], linear transportation costs td, gross utility s. A consumer is able to buy from a firm if and only if he has received advertising from it. ϕi – fraction of consumers receiving advertising from firm i

Advertising costs: Ai = Ai(ϕi) = 2

2 iaϕ

Potential market for firm 1: ϕ1. Out of these consumers, a fraction (1 – ϕ2) have not received any advertising from firm 2. The rest, a fraction ϕ2 out of ϕ1, know about both firms. Firm 1’s demand:

D1 = ϕ1 ( )

−++−t

pp

221

1 1222 ϕϕ


A simultaneous-move game. Each firm chooses advertising and price. Firm 1’s problem:

( ) ( ) 21

1222111

, 2221

1max11

ϕϕϕϕπϕ

a

t

ppcp

p−

−++−−=

Two FOCs for each firm.

FOC[p1]: ( ) ( ) 0222

11 21

112

221 =−−

−++−t

cpt

pp ϕϕϕϕϕ

FOC[ϕ1]: ( ) ( ) 022

11 1

12221 =−

−++−− ϕϕϕ at

ppcp

⇒ ( )2

21 21

ϕt

tcpp +−+=

( ) ( )

−++−−=t

ppcp

a 221

11 12

2211 ϕϕϕ


Firms are identical ⇒ Symmetric equilibrium

( )ϕt

tcpp +−+=21

⇒

−+= 12ϕ

tcp

( ) ( )

+−−=21

11 ϕϕϕ cpa

−

−=2

1121 ϕϕ

ϕ ta

⇒

t

a21

2

+=ϕ

Condition: 21≥

t

a

⇒ p = c + at2 Condition: s ≥ c + t + at2 (≥ c + 2t)

• 0<∂∂

a

ϕ, 0>

∂∂a

p


Firms’ profit:

( )221

2

t

a

a

+=π

• 0>∂∂

t

π; 0>

∂∂

a

π!

An increase in advertising costs increases firms’ profits. Two effects of an increase in a on profits: A direct, negative effect. An indirect, positive effect: a ↑ → ϕ↓ → p↑ Firms profit collectively from more expensive advertising. Crucial assumption: convex advertising costs. What about the market for advertising? [Kind, Nilssen & Sørgard, Marketing Science 2009]


Social optimum Average transportation costs

among fully informed consumers: t/4. among partially informed consumers: t/2. The social planner’s problem:

( ) 22

22

212

4max ϕϕϕϕ

ϕ

atcs

tcs −

−−−+

−−

( )

( ) tacs

tcs

2

322

2*

−+−−−=ϕ

[Condition: t ≤ 2(s – c)] Special cases: (i)

t

a → 2

1 : ϕe → 1

ϕ* → ( ) tcs

t

−−−

41 < 1

Too much advertising in equilibrium

(ii) t

a → ∞: ϕe → 0

ϕ* → cs

a

−+1

1 > 0

Too little advertising in equilibrium


Vertical product differentiation Quality competition Consumers agree on what is the best product variant. But they differ in their willingness to pay for quality. s – quality θ – measure of a consumer’s taste for quality. If a consumer of type θ buys a product of quality s at price p, her net utility is: U = θs – p F(θ) – cumulative distribution function of consumer type F(θ’ ) – fraction of consumers with type θ ≤ θ’. Unit demand: If θs – p ≥ 0, then a consumer of type θ buys one unit of the good. One firm: At price p, its demand is D(p) = 1 – ( )

s

pF .


Two firms: Suppose s1 < s2, p1 < p2. The indifferent consumer: θ~s1 – p1 = θ~s2 – p2

12

12~ss

pp

−−=θ

Product 2 quality dominates product 1 if:

θ~ < 1

1

p

s ⇔ 2 1

2 1

p p

s s<

Otherwise 2 1

2 1

p p

s s

≥

, demand is:

D1(p1, p2) =

−−

12

12

ss

ppF –

1

1

s

pF

D2(p1, p2) = 1 –

−−

12

12

ss

ppF

Assume:

Consumers uniformly distributed across [θ, θ ]

Consumers sufficiently different: θ > 2θ (avoiding quality dominance in equilibrium)

Firm 2 is the high-quality producer: s2 > s1.

Production costs independent of quality: c


Equilibrium in prices

12

12~ss

pp

−−=θ

Firm 1’s profit: ( )

−

−−−=

1

1

12

1211 ,max

s

p

ss

ppcp θπ

Best response of firm 1:

( )

( )[ ] ( ) ( )( )

−+<

−+≥≥++−−+

++>+

=

122

122211222

1

21222

1

1

if ,

if ,

if ,2

1

sscpc

sscpsscsspc

sscppc

p

s

s

θθθθ

θ

Firm 2’s profit: ( )

−−−−=

12

1222 ss

ppcp θπ

Best response of firm 2:

( )[ ]1212

12 sspcp −++= θ


Equilibrium prices:

( )( )121 231

sscp −−+= θθ

( )( )122 231

sscp −−+= θθ

Condition for the market being covered, 1

1

s

p≥θ :

c ≤ 3

1 [θ(2s1 + s2) – (θ – θ)(s2 – s1)]

p2

c

c p1

BR2(p1)

BR1(p2)


• The high-quality firm sets the higher price:

p2 – p1 = 3

1 (θ + θ)(s2 – s1) > 0

• The high-quality firm has the higher demand:

12

12~ss

pp

−−=θ =

3

1 (θ + θ) < 2

1 (θ + θ)

D1 = θ~– θ = 3

1 (θ – 2θ)

D2 = θ – θ~ = 3

1 (2θ – θ)

• The high-quality firm has the higher profit:

π1(s1, s2) = (p1 – c)D1 = 9

1 (θ – 2θ)2(s2 – s1)

π2(s1, s2) = (p2 – c)D2 = 9

1 (2θ – θ)2(s2 – s1)

• Firms’ profits are increasing in the quality difference Two-stage game Stage 1: Firms choose qualities Stage 2: Firms choose prices Stage 1 – feasible quality range: [s, s]

Assume: c ≤ 3

1 [θ(2s + s) – (θ – θ)(s – s)]

In equilibrium: s1 = s, s2 = s (or the opposite).


• Asymmetric equilibrium • Maximum differentiation What if …

• c > 3

1 [θ(2s + s) – (θ – θ)(s – s)]

- the low-quality firm will choose a quality above s. • θ < 2θ

- only one firm active in the market: p1 = c, D1 = 0, π1 = 0

p2 = c + 2

1 θ (s – s), D2 = 1, π2 = 2

1 θ (s – s)

- natural monopoly: low consumer heterogeneity makes price competition too intense for the low-quality firm

Natural duopoly for a range of consumer heterogeneity “above” θ > 2θ. Vertical differentiation: the number of firms determined by consumer heterogeneity. Horizontal differentiation: the number of firms determined by market size.


Mergers Why merge?

• Reduce competition – increase market power.

• Cost savings – economies of scale and scope.

• But necessary to merge in order to get bigger? o Input factors in total fixed supply.

Why allow mergers?

• Cost savings o Oliver Williamson: the efficiency defense

Williamson’s point: It may not take a huge cost saving to dominate the deadweight loss from a merger.


But note:

• What if the pre-merger price is not competitive?

o Larger cost savings needed to outweigh deadweight loss.

• Production reshuffling: More of the production in the

industry will be made by the low-cost firm – an additional source of cost savings in the industry.

• What is the appropriate welfare standard? � consumer welfare standard � total welfare standard

• What are the long-term effects of the merger?

� R&D, capacity investments, new products, etc. � collusion


Static effects of mergers

• Unilateral effects

• In general, welfare analyses of mergers are complex – even within rather simple models.

• An alternative: a sufficient condition for a merger to be welfare improving

• The Farrell-Shapiro criterion A merger affects

• the merging firms � price � costs

• the non-merging firms � price

• consumers � price

When a merger is proposed, then – presumably – it is profitable for the merging firms. So the competition authority – when looking for a sufficient condition for a welfare-improvement – can limit the analysis to the merger’s effect on

(i) non-merging firms, and (ii) consumers

→ the external effect of a merger Cost savings affect to a large extent only the merging parties. So focusing on the external effect, we do not need to assess vague statements about cost savings from a merger.


If the merger leads to a higher price, then non-merging firms benefit, and consumers suffer. But what is the total external effect? A merger model with Cournot competition X – total output in the industry xi – firm i’s output yi – all other firms’ output: yi= X – xi Firm i’s costs: ci(xi) Inverse demand: p(X) Firm i’s first-order condition:

p(X) + xip’(X) – ci’(xi) = 0. ⇒

p(xi + yi) + xip’(xi + yi) – ci’(xi) = 0 Firm i’s response to a change in other firms’ output – total differentiation wrt xi and yi: �� = �� = − � + ��"2� + ��" − �" From which we find firm i’s response to a change in total output:

dxi = Ridyi ⇒ dxi(1 + Ri) = Ri(dxi + dyi) = RidX

⇒ �� = ��1 + �� = �� + ��"�� "�� − �′�� = −λ� < 0


Welfare effects of a merger Two sets of firms:

I – insiders O – outsiders

An infinitesimal merger

• dXI – a small exogenous change in industry output Change in welfare from this merger:

�� = �� − � � + �� − �′��∈�

• Changes in output assessed at market price p. • cI – insiders’ total costs • Note: dxi = – λidXI for each outsider firm • From an outsider firm’s FOC: p – ci’ = – xip’(X) • The external effect of the merger: dE = dW – dπI. • The market share of a firm: si = xi/X.

⇒

�� = �� + �� − � �� − �� + ��′��λ��∈�

�� = �� − �� = −�� + ��′��λ��∈�

�� = �� λ��∈�− �� = �� λ�!��∈�

− !� ��


Here, p’ < 0 and, typically, dXI < 0. So the external effect of a merger (the accumulation of many infinitesimal mergers) is positive if and only if:

i i Ii O

s sλ∈

>∑ !

→ An upper bound on the merging firms’ joint (pre-merger) market share in order for their merger to improve welfare. Examples 1. A simple model: constant marginal costs, linear demand

ci” = 0, p” = 0 → λi = 1. Before merger: all firms of equal size. The external effect is positive if the set of merging firms is less than half of all firms: I i

i O

s s∈

<∑ ⇔ m < n/2

• But: will such a merger be profitable?


2. A more sophisticated model: merger between “units of capital”. The Perry-Porter model.

Cost function: C(xi, ki) = "#$%&'$. Marginal costs:

()(#$ = "#$'$

Interpretation: k is an input factor that is in total fixed supply within the industry and not available outside the industry (such as “industry knowledge”). The only way for a firm to expand is to acquire k from other firms, such as through a merger. The more k a firm has, the lower are its costs – cost savings from mergers. A merger between two firms with k1 and k2 units of capital creates a firm with k1 + k2 units of capital.

Also assume linear inverse demand: P(X) = a – X. ⇒

ii

i

k

c kλ =

+

FOC for firm i:

p + xip’ – C’(xi) = 0 ⇔ 0i ii

cp x x

k− − = ⇔ i

i

xp

λ= ⇔

i ii

x s

pλ

ε= =

(since ε = – D’p/D = p/X when demand is linear)


The external effect is positive if:

21I i

i O

s sε ∈

< ∑

• The size of the external effect depends on how

concentrated the non-merging part of the industry is! • A merger is more likely to be welfare-enhancing if the

rest of the industry is concentrated. • A merger among small firms leads to the other, big, firms

expanding, which is good. (Production reshuffling) Criticism of the Farrell-Shapiro approach

• The presumption that the merger is privately profitable may not be valid

� Empire building � Tax motivated mergers � Pre-emption (or encouragement) of other

mergers


Coordinated effects of a merger

• A merger’s effect on collusion

• What effect does a merger have in an industry where firms collude? – On balance: unclear.

� The merging firms now earn more and have

reduced incentives to cheat on the collusive agreement after the merger – the merger makes collusion easier.

• But the picture is complicated: merging firms are bigger and often bigger incentives to break out of punishment phases – thus making collusion more difficult.

� The non-merging firms now earn more without

collusion and therefore have increased incentives for breaking out of the collusive agreement after the merger – the merger makes collusion more difficult.

Regulating mergers

• Merger policy

• The welfare standard


Entry How is the market structure determined in an industry? (number of firms, market shares, etc.) • Entry until profit equals zero

- But what with all the positive profits we observe? • Regulations

- But what with deregulations over the last decades? • Technology

- Economies of scale → natural monopoly • Vertical product differentiation

- natural oligopoly • The established (incumbent) firms’ strategic advantage Three strategies when confronted with an entry threat • Blockading entry: “business as usual” • Deterring entry: Established firms act in such a way that

entry is sufficiently unattractive • Accommodating entry


Technology vs. strategic advantages What kind of fixed costs? • Irreversible/Sunk costs: Strategic advantage • Reversible fixed costs: Economies of scale Contestability theory

Main thesis: economies of scale give only a limited advantage for the established firm Suppose costs are: C(q) = cq + f, if q > 0, 0, otherwise (reversible fixed costs)

qc

pc AC

D(p)


The incumbent firm sets price pc and quantity qc. This situation is sustainable in equilibrium because

- any p < pc by another firm yields a loss - any p > pc by the incumbent firm entails entry

What game is played here? • Prices before quantities? • Short-term commitment of capacity; “hit-and-run entry”.

- Short-term commitment means a small strategic advantage.

- If another firm enters, then the incumbent wants to leave as soon as possible.

- In order to prevent such entry, the incumbent may want to set q > qm.

- As the commitment period shrinks to zero, q → qc. [Tirole, pp. 340-341]


The strategic advantage of being incumbent • a simple model • a general analysis of business strategies How to treat an entry threat? A simple model

Two-stage game: Sequential moves. Stage 1: Incumbent (firm 1) chooses capacity. Stage 2: Potential entrant (firm 2) chooses capacity; zero capacity = no entry. Profit functions (gross of any entry costs): π1(K1, K2) = K1(1 – K1 – K2) π2(K1, K2) = K2(1 – K1 – K2) Ki = capacity choice of firm i.

21

2

KK

i

∂∂∂ π

< 0


Case (i): No entry costs (Stackelberg 1934) Accommodated entry

Stage 2: 2

2

K∂∂π

= 1 – K1 – 2K2 = 0

→ K2 = R2(K1) = 2

1 1K−

Stage 1: π1 = K1[1 – K1 – K2] = K1[1 – K1 – 2

1 1K−]

= ( )

21 11 KK −

→ sK1 = 21

; sK2 = R2(21

) = 41

.

π1 = 81

; π2 = 161

.

Comparison: Simultaneous moves – Cournot.

K1 = R1(K2) = 2

1 2K−

K2 = R2(K1) = 2

1 1K−

→ K1 = K2 = 31

; π1 = π2 = 91

.


Case (ii): Entry costs

f = entry costs. Entry cost not relevant for firm 1 – sunk cost. Profit function of firm 2 net of entry costs: π2(K1, K2) = K2(1 – K1 – K2) – f, if K2 > 0; = 0, if K2 = 0. Blockaded entry: K2 = 0. Stage 1: max π1(K1, 0) = K1(1 – K1).

→ mK1 = 21

.

But when is K2 = 0 the best response to K1 = 21

?

Stage 2: K2 = R2(21

) = 41

, or

0. Profit is:

π2 = π2(21

,41

) = 161

– f, or

0.

→ Entry is blockaded if: f ≥ 161

≈ 0.063.


Deterred entry Which stage-1 quantity makes firm 2 indifferent between entry and no entry? bK1

If K1 ≥ bK1 , then firm 2 chooses no entry. Stage 2:

2

maxK

K2(1 – bK1 – K2) – f

→ K2 = 2

1 1bK−

.

→ 2maxπ = [

21 1

bK−]{1 – bK1 – [

21 1

bK−]} – f

2maxπ = 0 → fK b 211 −=

Stage 1:

f ≥ 161

→

bK1 ≤ mK1 , and firm 1 prefers mK1 to bK1 ; blockaded entry.

f < 161

→

By setting K1 = bK1 , firm 1 deters entry and earns: π

1( bK1 , 0) = bK1 [1 – bK1 ]

= ( f21− )[1 – ( f21− )]

= ff 42 −


Alternatively, firm 1 can accommodate entry and earn 81

(Stackelberg). → Entry deterrence better than entry accommodation when:

π1( bK1 , 0) >

81

ff 42 − > 81

⇔ 032

1

2

1 <+− ff

⇔ 32

1

16

1

2

1 <+− ff

⇔ 32

1

4

12

<

−f

[We are interested in the case f < 1/16, that is, f – 1/4 < 0. Taking squares, we

are interested in the absolute value of f - 1/4, that is 1/4 – f . So:

⇔ 24

1

4

1 <− f ⇔

−>2

11

4

1f ]

⇔

−=

−> 22

3

16

1

2

11

16

12

f ≈ 0.0054


→ What the incumbent chooses to do in face of an entry threat depends on the entry costs: (i) Low entry costs imply accommodated entry:

f ∈ [0,

− 22

3

16

1]

K1 = 1/2, K2 = 1/4. (ii) Medium-sized entry costs imply deterred entry:

f ∈ (

− 22

3

16

1, 16

1)

K1 = f21− , K2 = 0. (iii) High entry costs imply blockaded entry:

f ≥ 161

K1 = 1/2, K2 = 0.


How to treat an entry threat? A more general model Two firms:

firm 1 – the incumbent firm 2 – the potential entrant

Stage 1:

Firm 1 chooses K1. Firm 2 decides whether or not to enter.

Stage 2: Either:

(i) firm 1 is a monopolist, or:

(ii) both firms are in the market and choose their stage-2 variables x1 and x2 simultaneously.

Stage-2 equilibrium: {x1(K1), x2(K1)} Comparative statics How is stage-2 equilibrium affected by the incumbent’s stage-1 move K1? Can we apply comparative statics to an equilibrium?

- uniqueness - stability


Stability: dynamic reasoning in a static model If the stage-2 game changes, then also the stage-2 equilibrium changes. But will the model stabilize at the new equilibrium?

( )12 xR

( )��21

xR


Stability condition: ”R1 crosses R2 from above” or: R1 steeper than R2, as we see them.

( ) ( )*12*

21

''

1xR

xR−>−

⇔ R1’(x2*) R2’(x1*) < 1

122

2221

22

21

1221

12

<∂∂

∂∂∂∂∂

∂∂∂⇔x

xx

x

xx

ππ

ππ

021

22

21

12

22

22

21

12

>∂∂

∂∂∂

∂−∂

∂∂∂⇔

xxxxxx

ππππ

Firms’ stage-2 profits: π1(K1, x1*(K1), x2*(K1)) and π2(K1, x1*(K1), x2*(K1)) What does firm 1 do at stage 1? • If π2(K1, x1*(K1), x2*(K1)) ≤ 0, then firm 1 has made a

choice of K1 at stage 1 that deters entry. • If π2(K1, x1*(K1), x2*(K1)) > 0, then firm 1 has made a

choice of K1 at stage 1 that accommodates entry.


Entry deterrence

In order to deter entry, firm 1 must set K1 such that π2 = 0. What is the effect on π2 of a change in K1? π2 = π2(K1, x1*(K1), x2*(K1))

�1

*2

0

2

2

1

*1

1

2

1

2

1

2

dK

dx

xdK

dx

xKdK

d

=

∂∂+

∂∂+

∂∂= ππππ

� ��

effectstrategic

1

*1

1

2

effectdirect

1

2

1

2

dK

dx

xKdK

d

∂∂+

∂∂= πππ

Stage-1 choices with a direct effect:

- location - advertising - not capacity

Firm 1 wants π2 so low that π2 = 0. • If dπ2/dK1 < 0, then π2 = 0 is obtained by increasing K1,

that is, by being big. The strategy is to look aggressive by being big: the top dog strategy

• If dπ2/dK1 > 0, then π2 = 0 is obtained by reducing K1,

that is, by being small. The strategy is to look aggressive by being small: the lean-and-hungry-look strategy


Entry accommodation The optimum choice for firm 1 at stage 1 is such that firm 2’s profit after entry is positive: π2(K1, x1*(K1), x2*(K1)) > 0 Since entry is inevitable, firm 1 seeks to maximize own profit, given entry by firm 2. π1 = π1(K1, x1*(K1), x2*(K1))

�1

*2

2

1

1

*1

0

1

1

1

1

1

1

dK

dx

xdK

dx

xKdK

d

∂∂+

∂∂+

∂∂=

=

ππππ

� ��

effectstrategic

1

*2

2

1

effectdirect

1

1

1

1

dK

dx

xKdK

d

∂∂+

∂∂= πππ

Suppose 1

1

K∂∂π

= 0: no direct effect


The strategic effect Assume firms’ stage-2 actions are symmetric: one firm’s effect on the other firm’s profit is qualitatively the same for the two firms.

∂∂=

∂∂

1

2

2

1

xsign

xsign

ππ

From the chain rule:

( )1

*1*

121

*1

1

*2

1

*2 '

dK

dxxR

dK

dx

dx

dx

dK

dx ==

⇒

( )�

curve response

-best slope

2

deterrenceentry effect, strategic

1

*1

1

2

ionaccommodatentry effect, strategic

1

*2

2

1

'RsigndK

dx

xsign

dK

dx

xsign ⋅

∂∂=

∂∂

��

ππ


(i) Stage-2 variables are strategic substitutes: R2’ < 0.

Example: quantity competition at stage 2.

∂∂−=

∂∂

1

*1

1

2

1

*2

2

1

dK

dx

xsign

dK

dx

xsign

ππ

If an increase in K1 reduces π2, then it increases π1. If an increase in K1 increases π2, then it reduces π1. With strategic substitutes, entry accommodation and entry deterrence are the same thing.

It is good for firm 1 to be aggressive at stage 1, also when it accommodates entry. The strategy is, either:

to look aggressive by being big: the top-dog strategy,

or

to look aggressive by being small: the lean-and-hungry-look strategy


(ii) Stage-2 variables are strategic complements: R2’ > 0.

Example: price competition at stage 2.

∂∂=

∂∂

1

*1

1

2

1

*2

2

1

dK

dx

xsign

dK

dx

xsign

ππ

If an increase in K1 reduces π2, then it also reduces π1. If an increase in K1 increases π2, then it also increases π1.

An entry-accommodating incumbent firm now wants to be non-aggressive!

If firm 1 becomes aggressive when K1 is large, then it now wants to keep K1 down in order to look non-aggressive:

the puppy-dog strategy.

If firm 1 becomes aggressive when K1 is small, then it now wants to have a high K1 in order to look non-aggressive:

the fat-cat strategy.


Business strategies

I. Entry deterrence

Incumbent looks aggressive when investment is

big

small

Top Dog

Lean and Hungry Look

II. Entry accommodation

Incumbent looks aggressive when investment is

big

small

strategic

complements

Puppy Dog

Fat Cat

strategic substitutes

Top Dog

Lean and Hungry Look


Applications:

i) Two-stage model: 1) capacities 2) prices

Prices strategic complements.

Large capacity makes a firm aggressive.

→ Puppy dog strategy: Install a rather small capacity in order to soften the ensuing price competition

ii) Location model: 1) location 2) prices

Again: prices are strategic complements

Interpret K1 as closeness to the centre.

→ Puppy dog strategy: Locate far away from the centre in order to soften the ensuing price competition


iii) Puppy-dog entry

Stage 1: Entrant decides capacity and price Stage 2: Incumbent decides price

Incumbent’s options: • monopoly on residual market: π = A + C • undercut and get the whole market: π = B + C

Entrant’s optimum decision: Choose p and Q such that A > B. [Gelman and Salop, ”Judo Economics: Capacity Limitation and Coupon Competition”, Bell Journal of Economics 14 (1983), 315-325]

A Norwegian example: Viking Cement, 1983. [Sørgard, ”A Consumer as an Entrant in the Norwegian Cement Market”, Journal of Industrial Economics, 41 (1993), 191-204]

xM

cM

pM

p2

c2

�

Q

D(p) – Q D(p)

A

C

B


iv) Persuasive advertising Stage 1: Incumbent invests in loyalty-inducing advertising Stage 2: Price competition (if entry) Entry deterrence: look aggressive High investments → Many loyal firm-1 customers in stage 2 → High price by firm 1 ⇒ Lean and Hungry Look: In order to deter entry, the incumbent firm keeps its advertising low in order to keep post-entry prices, and therefore firm 2’s post-entry profit, low. Entry accommodation: look non-aggressive Firm 1 wants to have many loyal customers, so that its incentives to set a low price in stage 2 are weak. ⇒ Fat Cat strategy Example: the Norwegian ice-cream market 1992 NM (Norske Meierier) vs GB. High level of advertising by NM. Not because NM wanted to keep GB out, but because it wanted to keep GB’s prices high (Fat Cat).

Merger Control: COOP’s acquisition of ICA

Guest Lecture at University of Oslo

March 17 2016

Lars Sørgard

The Norwegian Competition Authority

17.03.2016 Sørgard Merger Control University of Oslo 1

The text today

• Briefly about merger control

– Conditions for blocking a merger

– Some examples

• Theory for the price effect of a merger

– Why market shares can be misleading

– The concept ‘closeness of competition’

• Example: COOP’s acquisition of ICA

– Some facts about the case

– How to analyse closeness of competition



Merger control in Norway

• If over a threshold level, must report M&A to

Konkurransetilsynet (KT)

– 1 MRD jointly and100 MNOK for the smallest in annual turnover

– But Konkurransetilsynet can also block a merger not reported

• Deadlines

– 70 working days to statement of objections (begrunnet varsel)

– Then 15 working days for the parties and KT each before decision

– Appeal to the ministry (from 1.1.17: Independent appeal body))

• If not accepted, two possible outcomes

– Block the merger

– Accept it given remedies (structural vs behavioral remedies)

0

1

2

3

4

5

6

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Forbud Godkjent på vilkår

Rather large # of decisions

• More active enforcement of merger control in

Norway than in most other countries

– Decisions on almost 3 mergers annually 2004-15

Sørgard Merger Control University of Oslo 4

Merger control decision2004-15

17.03.2016

The most recent examples• Three most recent bans:

– June 2014: Norsk Gjenvinning’s acquisiiton of Avfall Sør Bedrift

– March 2013: Retriever and Innholdsutvikling

– Jan 2013: Nor Tekstil and Sentralvaskeriene

• Five mergers accepted with remedies in 2015:

– September 2015: Aleris acquires Teres (private hospital)• Accepted given sales of hospitals in Trondheim and Tromsø

– August 2015: Orkla acquires Cederroth• Accepted given sales of the brand Asan

– July 2015: St1 acquires Shell• Accepted given that St1 sells all its petrol stations

– March 2015: COOP acquires ICA• Accepted given sales of 93 ICA grocery stores

– February 2015: TeliaSonera acquiresTele2• Accepted given that TeliaSonera, among others, signs a roaming agreement with ICE and

sells mobile network and Network Norway to ICE.


The condition for an intervention

– ‘.. vil føre til eller forsterke en vesentligbegrensning av konkurransen i strid med lovens formål’

• Two conditions:1. ‘en vesentlig begrensning av konkurransen’2. ‘i strid med lovens formål’

• Condition 1 is (almost) identical to EU• Condition 2 special for Norway

– Norway a total welfare standard, while most countries a consumer welfare standard

– (Stortinget decided last week to shift to a consumer welfare standard)


The text today



– Some examples








Traditional vs new approach

• Common to define relevant market and usemarket shares in the competitive asessment

– Market delineation not a goal, but a mean to understand the toughness of competition

– # of firms and market shares can be a goodproxy for market power in some industries

• New method for markets with differentiatedproducts

– Market shares can over/underestimate marketpower; how close rivals the merging parties are

– Closeness of competition the key issue


Ex.: Somerfield case in England

• In 2005 Somerfield acquired 115 Safeway

grocery stores from Morrison

• Local competition, so they analysed the effect

of each acquired store

• Stage I of the analysis (OFT):

– 23 of the acquired stores problematic

– Passed on the case to Competition Commission (CC)

• Stage II of the analysis (CC):

– Further inquires of 56 stores, and asked Somerfield

to sell out14 stores


Stage1: Trad. analysis

• Applied isochrone analysis to delineate themarket– Draw a circle around a store, and the size of the

circle determined by driving time

– Counted the # of rivals after the merger

– If three or less rivals after the merger, the mergerwas problematic

• Different rules for different stores– One-stop shopping 10/15 min travel time city/rural

– Smaller stores 5/10 min travel time city/rural

• Found 1 one-stop shopping and 22 smallerstores as problematic


Stage 2: Close rivals?• Isochrone analysis fail to take into account:

– Geographic differentiation; 0-1 decision

– Product differentiation; different store types


• CC used another

method to

– To detect how close

rivals they are

– Diversion ratio crucial

Closeness of competition and

price changes after merger

• Each firm price according to marginal cost

• Type of cost saving of importance– Savings in fixed costs not relevant

– Change in marg. cost relevant for price setting

• Farrell/Shapiro (2010): Upward Price Pressure (UPP)

• Upward Price Pressure (UPP) after a merger?– Lower marginal cost; Downward price pressure

– Close rivals; Upward price pressure


Upward Price Pressure (UPP)?

• Assume Bertrand w/diff. products

• One product each for firm 1 og 2, and joint profits

after the merger is (assuming only change in c1):

• How large reduciton in c1 for P1 not to

change?


0P

qcP

P

qcPq

1

20

22

1

1M

111

• Can apply the first order condition for

product 1 before the merger:

1

10

111P

qcPq

2

0

221

M

11 qcPqcP

UPP forts.

• The price of product 1 will not change if:


1

1

1

2

0

221

0

1 )(

Pq

Pq

cPcc M

= Fraction of those

leaving 1 that divert

to 2

• D12 = (Negative of ) Diversion from

product 1 to product 2

Cost

reduciton

11

1212

/

/

pq

pqD

UPP cont..

– E1 = reduction in marginal cost for product 1

• Condition for UPP on product 1:


1112

1UPP

L

LED

• Rearranging:

12

0

221

0

1 )( DcPcc M

Cost

reduction

Diversion

ratio

Price-cost margin on

product 2

)1(

)2(

How to find (2)

• Define as follows:


– E = reduction in mc:

• We can rearrange (1):

Eccc M 011

01

L

LE

p

cp

p

cpp

E

p

cp

p

c

Ecp

cED

1

0

0

0

0

0

0

• Then we have shown how we go

from (1) to (2)

UPP cont.• But the expression will underestimate

UPP

– Higher product 2 price makes it profitable to

increase price on product 1, and vice versa

– Lower mc for product 2 makes it profitable to

increase producct 1 price , and vice versa

• Taking this into account, it is found that

UPP on both products if:

17

L

L1E

D1

D

17.03.2016 Sørgard Merger Control University of Oslo

UPP cont.

• How large UPP (for a given change in marginal cost) determined by two factors:1. How large diversion to the other merging parties’

product?

2. How large price-cost margin on the sale that is recaptured?

• Other concepts that are analogous to UPP:– GUPPI (Gross Upward Pricing Pressure Index)

– IPR (Illustrative Price Rise)

– …

• But for all of them, 1 and 2 above is valid– Must consider 1) diversion ratios and 2) margins


UPP for product 1 after merger

• Product 117.03.2016 Sørgard Merger Control University of Oslo 19

• Product 2

• Optimal price ex ante– Loss = Gain for product

1, and sets price P1

• Incentive to set higher price onproduct 1 ex post merger– Will now recapture some of the

sales lost from product 1

• Value of diversion to product 2, when P1 increasesP1

P2

If firm A acquires firm C

• Crucial how large fraction of A’s customers

that has C as their second choice

– We do not have to find the market shares!


AC

B D E

The approach – in practice

• Applies a condition similar to one of those wehave shown– Can assume that the price on both products will

increase

– Quite common to consider UPP, given no change in marginal cost (then applying GUPPI)

• Then checking other aspects not captured by this approach– Low barriers to entry?

– How will rivals’ respond?

– Buyer power (partly captured by margin?)

– Repositioning of products ex post merger?


How to detect diversion ratios?• Econometric study (revealed preferences)

– Demand estimation is challenging

– Deadlines in merger cases

• Shock analysis– Effect of, say, sales campaigns

• Surveys among customers (stated preferences)– Used a lot in England, and Norway

• Internal documents– US: Counting how often rivals are mentioned

• Churn data– Can see from data where consumers divert

– Used in mobile phone merger in EU/Norway


Ex.: Diversion ratios vs market shares

in mobile phone market in Norway

Sørgard Wireless in Europe 22022016 23

Company Market share

Telenor 50 %

TSN 23 %

Tele2 18 %

Others 9 %

• Market shares bad proxy

for small players’ role?

– New, small players pick up

rather large fraction of

switchers

Diversion ratios from churn data:From/to TSN Tele2 Telenor Others

TSN 34 % 56 % 10 %

Tele2 30 % 60 % 10 %

Telenor 35 % 44 % 21 %

Others 21 % 25 % 54 %

The text today



– Some examples








The transaction

• Coop acquired all the shares in Ica Norge

– 03.10.2014: Agreement

– 05.11.2014: Reported to Konkurransetilsynet

– 04.03.2015: Deadline for 70 days SO

– 12.05.2015: Deadline for final decision

• Konkurransetilsynet accepted it with remedies

– 11.02.2015: Coop offered remedies

– 03.03.2015: A revised offer

– 04.03.2015: Accepted with remedies

• Had to sell out 93 stores

• Not allowed to complete the deal before this was done


The parties

COOP:

• 22,9 % nationalmarket share in 2013

• Integrated procure-ment and distribution

• Nation wide

• Lowprice, super-market, local stores and hypermarket

• ICA:

• 10,4 % national marketshare in 2013

• Integrated procure-ment and distribution(agreement with NG, butnot implemented)

• Nation wide

• Lowprice, super-market and localstores


The grocery market - Norway• 5 chains with one or more type of stores each

• 4 integrated chains (wholesale and retail)

• Product market: Groceries sold throughgrocery stores, including all types of stores

• Both a national and a local dimension

• They compete along several dimensions– Price

• Max prices are (mainly) set at the national level

• Prices varies between local areas

• Possible to change prices quickly in local markets

– Other dimensions• Service, product range and quality

• These can be changed in each local store


Lavpris60 %

Supermarked25 %

Nærbutikker10 %

Hypermarkeder5 %

Sørgard Merger Control University of Oslo 28

Local markets w/national firms

50 % market share nationally

100 % market share locally

50 % market share nationally

50 % market share locally


The counterfactual• Must show a causality from the acqusition

to the dampening of competition

• What is the most likely market structure ifno acquisition?

• In most cases: Status quo

– Market condition at the time of the merger

• Case-by-case evaluation

• Konkurransetilsynet in this case:

– Ica stays in the market, but will scale down

– Ica buyer agreement with Coop or Rema 1000



Changes due to the acquisition

• Retail, nationally:– # 3 acquires one of the two smallest

– A change from four to three chains

– Inceased symmetry (collusion?)

• Wholesale, nationally:– No change; three integrated chains

• Locally:– Appr. 550 Ica stores acquired by Coop

– Many local markets affected


Which local markets?

• Screening of markets

– Coop 800 stores, Ica 550 stores

– Identified unproblematic local markets

• The parties no overlap

• Parties small compared to other chains

• All other chains are in the area

• Left with166 Ica- and 178 COOP stores in 125 geographic areas


Which local markets cont.

• Used data from a map program – Distance between parties’ stores

– Distance to the rivals’ stores

– Data on where cities and villages are

• Data from Coop on where their customers live

• Information about the stores: – Size

– Type of store

• Internal documents


GUPPI in remaining markets

• GUPPI= D12 ∗P2

P1∗ m2

• GUPPI over 3 %: Problematic market

• No prediction of price increase

• GUPPI can lead to:

– Higher prices

– Lower quality (opening hours and # of people employed)

• 𝐷12𝑐𝑟𝑖𝑡 = 0.03/(𝑚2 ∗ 𝑃2/𝑃1)

• Must also consider other factors


Relativ

margin

How to measure closeness of

competition?

• Asked shoppers, and from that estimated diversion ratios:

• “Tenk deg at du før avreise til butikken vissteat [konkret navn på butikken] var stengt, hvor ville du da handlet?

– Survey outside 60 stores with 200 respondents for each store

– Simple OLS models applied to find out what will affect closeness of competition in other local markets


DN 10.01.15: Study to detect

diversion ratios paid by COOP


How to find margins

• Which cost will vary with a small change in quantity sold?

• Input price

• Other costs (labour, distribution etc)

• Information from the parties used to estimate margin in each store


Other aspects

• Likely, efficient and timely entry– Generally high barriers to entry for new

players

– If other chains had entry plans, that taken into account

• Rivals’ response to a price increase– An argument for further price increase in

Bertrand market with differentiated products

• Savings on marginal costs– The parties the burden of proof

• (buyer power)


Coop/ICA: How it ended

• The parties had 1350 stores

• 125 areas identified after first

screening as problematic

• After a closer analysis, 90 areas

remained as problematic

– The method we have shown (UPP)

crucial for the choice of local markets

• The parties had to sell out 93 stores


Thank you!


Merger ControlExamples from practice

Jostein Skaar

April 13, 2016

Outline

UiO April 13 20162

Efficiencies

Market definition

Unilateral effects

• Egmont/CMore

• Telia Sonera/Tele 2

• Aleris/Teres

• Orkla/Cederroth

• Telia Sonera/Tele 2

• Sats/Elixia

1

2

3

CasesTopic Analysis

• Simple theory and facts

• Shock analysis

• UPP

• Cost estimates

• Type of efficiencies

• Welfare standard

Motivation:

Example from last week – presentation in Denmark

3 UiO April 13 2016

1. Unilateral effects

- Intuition for the method

- Our findings

2. ……….

Agenda

Unilateral effects

• When firm A raises its price, it looses customers to competing firms (grey arrows).

– How many customers e.g. Firm B gains, depends on how close a substitute Firm B’s product is (diversion).

• However, when Firm A raises its price, it also earns more money per customer. Firms “balance” these two effects in order to maximise profit.

5

Why do they matter in a merger?

Firm A

Firm B

Firm C

Firm D

Firm E

UiO April 13 2016

So what happens if Firm A and Firm B merge?

Unilateral effects

• If Firm A and Firm B merge, Firm A no longer looses all customers from the same price increase, because some of the customers go to Firm B.

– A price increase now becomes more profitable than before the merger.

– How much more profitable the price increase becomes, depends on the diversion from A to B (the size of the blue arrow).

– A larger diversion, all else equal, leads to a larger incentive to raise prices.

6

Why do they matter in a merger?

Firm A

Firm B

Firm C

Firm D

Firm E

UiO April 13 2016

Firms can regain lost profits from a price increase,

leading to an incentive to raise prices

What influences the magnitude of unilateral effects?

• Large diversion ratio = large pricing pressure

– Because the larger the diversion from A to B, the more profit Firm A can regain through Firm B

– End result: the more competitive (closer substitutes) Firm A and B are pre-merger, the higher the pricing pressure

• Margins matter for other firm’s pricing pressure

– Even if e.g. all customers go to Firm B if A raises its price, it will not be profitable if Firm B’s margin is zero.

– End result: The merged firms shift sales towards the relatively more profitable product.

7

The significance of diversion ratios and margins

Firm A

Firm B

Firm C

Firm D

Firm E

UiO April 13 2016

Unilateral effects of a XX – YY merger

8

• We find large pricing pressures for both XX and YY, given assumptions about:

– Diversion ratios

– Market size

– Margins

UiO April 13 2016

What if marginal costs (margins) change? This is a key assumption for our findings.

What happens if diversion

ratios are smaller?• Pricing pressures are reduced

• Despite assuming small

diversion ratios, the pricing

pressures remain large

What if the Market is larger?• Pricing pressure for YY increases,

because profit can be regained in

several (not just one) ………

• Pricing pressure for XX decreases,

as the diversion from YY is reduced

with more competitors

Market definition –Closeness of competition: Aleris/Teres – private hospitals

9 UiO April 13 2016

Who are competing – hospital services

10

• Main question: Are private hospitals like Aleris and Teres competing with publicly financed hospitals?

• Some information (facts) from the SO (Statement of Objection)

– Norway is divided into four health regions (North, Middle, South East and West)

– In each region the hospitals are owned by a separate regional business unit (RHF)

– The RHF is responsible for necessary health services to the population within the region

– In order to fulfill this obligation they buy services also from private hospitals

– Services from private hospitals are bought through tenders

UiO April 13 2016

More information from the SO

11

• Private hospitals compete for rights to supply hospital services that are publicly financed – by the RHF

• Private hospitals need to have a public concession in order to participate in the competition

• In this specific market Aleris and Teres have overlapping activities – orthopedics, plastic and obesity surgery

• After the tender has been concluded, private hospitals with agreements compete with public hospitals with regard to who actually performs the operation

• Competition between public and private hospitals if public hospitals also provide the relevant services

• Based on these facts the NCA defines a separate market for tenders from private hospitals –any competition from public hospitals will be considered later in the analysis – competition assessment

UiO April 13 2016

Our analysis - market share – public hospitals

12

Tabell 1: Markedsandeler (avrundet) offentlige sykehus – utvalg av alle DRG-er som er

knyttet til ortopedi, plastikk kirurgi og fedmekirurgi

Ortopedi Plastikk

kirurgi

Fedme-

kirurgi

Sør-Øst 99% 96% 97%

Vest 98% 96% 99%

Midt 96% 82% 86%

Nord 98% 96% 99%

Market shares – public hospitals – DRG points related to orthopedics, plastic and obesity surgery

UiO April 13 2016

RHF – optimal production

UiO April 13 201613

MC-public hospitals

With obligation to cover demand

DRG-financing

Production with no obligation and no use of private firms

• With no obligation to supply health care the

regional health unit would increase production

only until the marginal revenue (DRG-

financing) equals marginal cost – behaving as

a profit maximizing entity

• If they have an obligation (as they have - from

the owner – state) to produce more than this,

then their purpose would be to minimize cost to

reach the necessary level of production -

minimizing society cost involved in production

of health services

• If the marginal cost in production is higher than

what they have to pay private hospitals they

should buy services from private suppliers

Use of private hospitals 1

UiO April 13 201614

• Suppose that a private hospital can offer a price equal to the marginal cost of public production

– In this case the RHF should cancel he tender process and produce the necessary amount of services themselves

– If they accept the offer, they would have to pay more for the additional operations compared to own production – market area

Price- private

DRG-financing



MC-public hospitals

Use of private hospitals 2

UiO April 13 201615

• The RHF should only accept the offer if the price is sufficiently below marginal cost

– Accept the offer if the blue area is less or equal to the orange area

• The private hospitals are disciplined directly by the alternative for public hospitals – own production

• There is competition between public and private hospitals in the tender market

Price- private



MC-public hospitals

Competition in the «after» market

UiO April 13 201616

• Additional competition for patients after the tender has been concluded

• The private hospital has only won a right to treat patients with public financing – they would of cause try to supply as much as possible

• Knowing the price from private hospitals the RHF now are able to reduce cost more simply by treating patients where the marginal cost of own production is below the price offered and accepted by private hospitals

Price- private



MC-public hospitals

Flexibility in public production

UiO April 13 201617

Change in number of DRG points in public hospitals from 2013 to 2014

Number of publicly financed DRG points in private hospitals

Tele 2/TeliaSonera (Telia)

18 UiO April 13 2016

TeliaSonera gets approval of Tele2 acquisition in Norway

UiO April 13 201619

“I am pleased that the Norwegian Competition Authority sees the advantages with this transaction. This is good, not only for our and Tele2's customers, but

also for Norway as a whole. We will be a stronger and more credible alternative to Telenor on their home market. We will now further accelerate the roll-out of

mobile Internet”

- Johan Dennelind, President and CEO of TeliaSonera

Horizontal merger – TeliaSonera/Tele2

Unilateral effects

Coordinated effects

TeliaSonera + Tele2

Commitments

Efficiencies

Welfare effects

Competition – markets for

mobile phone services

Wholesale market

End-user market


Tele 2 lost necessary frequency rights in 2014

UiO April 13 201621

In addition:

High roaming cost for Tele 2 irrespective of loss of frequencies

Possible agreement to use TeliaSonera’s network in the counterfactual situation

References – UPP analysis

UiO April 13 201622

• Farrell, J., & Shapiro, C. (2010). Antitrust Evaluation of Horizontal Mergers: An EconomicAlternative to Market Definition. The B.E. Journal of Theoretical Economics, 10(1).

• Hausman, J., Moresi, S., & Rainey, M. (2011). Unilateral effects of mergers with general linear demand. Economics Letters, 111, ss. 119-121.

• The European Commission. (2012). Case No COMP/M.6497 - Hutchison 3G Austria / Orange Austria. Strasbourg: The European Commission.

• Decision V2015-1 – Norwegian Compeititon Authority

Basic UPP analysis

UiO April 13 201623

TSN+T2

TSN Tele 2

𝑫𝑻𝟐,𝑻𝑺𝑵

PT2 - GUPPI: Measuring incentive to

increase price on one product

- UPP (Hausman et al.): Unilateral

effect – optimal change in price of

one product

Hausmans et al. (2011)'s UPP-framework

UiO April 13 201624

Assumptions

• Linear demand

• Equilibrium according to first order conditions before the merger

• Other firms hold their prices unchanged

First order cond. before merger

First order cond.after merger Calculating UPP

• Price pressure

estimated based on

optimal pricing after

the merger

• Two equations and two

unknown variables

(Δ𝑝1

𝑝1,Δ𝑝2

𝑝2)

UPP for both

firms

FOC after merger• Need only parameters

before the merger to

calculate first order

conditions after

• Parameters: prices, cost,

diversion ratios and

quantities sold before

the merger

Possible counterfactual situation

UiO April 13 201625

Adjusted UPP – TeliaSonera/Tele2

UiO April 13 201626

• Hausman et al. (2011) deduces a formula to calculate unilateral effects

– Marginal cost is the same for both firms before and after the merger

– Does not incorporate vertical relationship before the merger

• In our analysis of the TSN/Tele2 aquisition we assumed that:

1. Tele2 had significant roaming costs before the merger – after the merger, no roaming cost

2. Before the merger TSN received roaming payment from Tele2

• Hausman et al. (2011) compares the first order conditions before and after the merger

– We used the same basic method adjusted for 1. and 2. above – adjusted UPP

• Adjustment important for UPP calculations

– Reduction in marginal cost implies a significant lower UPP for Tele2

– Roaming income received by TSN reduces the price pressure for TSN significantly

UiO April 13 201627

Assumptions –Tele2`s marginal cost after the merger

No change in MC No NRA or MVNO cost after the mergerAssumptions – counterfactual

scenario

Tele2 - MNO: Historic market shares, NRA prices and traffic

Tele2 - MVNO (1):No strategic links to TSN

Tele2 - MVNO (2): Strategic links to TSN through MVNO agreement

𝑼𝑷𝑷𝑴𝑪+ 𝑹𝑪𝑴𝑵𝑶 𝑼𝑷𝑷𝑴𝑪

𝑴𝑵𝑶

𝑼𝑷𝑷𝑴𝑪+ 𝑹𝑪𝑴𝑽𝑵𝑶 𝒏𝒐 𝒍𝒊𝒏𝒌 𝑼𝑷𝑷𝑴𝑪

𝑴𝑽𝑵𝑶 𝒏𝒐 𝒍𝒊𝒏𝒌

𝑼𝑷𝑷𝑴𝑪+𝑹𝑪𝑴𝑽𝑵𝑶 𝒍𝒊𝒏𝒌 𝑼𝑷𝑷𝑴𝑪

𝑴𝑽𝑵𝑶 𝒍𝒊𝒏𝒌

Tele2 and ICE - MNO: New NRA prices and strategic link to TSN 𝑼𝑷𝑷𝑴𝑪+ 𝑹𝑪

𝑴𝑵𝑶𝒘𝒊𝒕𝒉 𝑰𝑪𝑬 𝑼𝑷𝑷𝑴𝑪𝑴𝑵𝑶𝒘𝒊𝒕𝒉 𝑰𝑪𝑬

Comparing the standard UPP with the adjusted UPP

UiO April 13 201628

Reality

UPP

Time

𝑡1

𝑡2

price

cost

diversion

quantity

price

cost

diversion

quantity

Input data

Estimate: Price

pressure

Estimate: Price

pressure

UPP adjusted

1 2

Use an equilibrium model to test the two different indicators (based on Shubik & Levitan utility function)……

Merger between two vertically integrated firms – no change in marginal cost

UiO April 13 201629

Merger between two vertically integrated firms – change in marginal cost

UiO April 13 201630

One firm closes down the upstream activity and starts to buy input from a competing firm

UiO April 13 201631

Merger between firms with vertical relationship

UiO April 13 201632

Concluding remarks

UiO April 13 201633

Adjusted UPP

UPP (Hausman)

Step1:

Step2:

Step 1&2 (Δ𝑐2):

Estimates too high price pressure on product 2. Too high or too low price pressure on product 1.

Wrong estimates of price pressure on both products if asymmetric diversion ratios.

Results equal to the equilibrium model

N/A

One firm closes down the up-stream activity and starts to buy input from a competing firm

Merger between the firms in step 1

Merger between two vertically integrated firms –change in marginal cost

Unilateral effects – Sats/Elixia

UiO April 13 201634

Need marginal cost to calculate margins….

UiO April 13 201635

• Suppose that marginal cost is equal to average variable cost (Case No COMP/M.6497 -Hutchison 3G Austria / Orange Austria.)

• Identify the cost components that vary with a small change in production…..

• If 100% variable – average variable cost = marginal cost

• …it is not always obvious which costs that vary with production and how much

• Alternative solution used in the SATS/ELIXIA case (Finland)

– Use econometrics to estimate variable cost

Illustration – estimating variable cost

UiO April 13 201636

• Historic cost levels and volumes for one firm with two branches

• The blue lines represent the result of the regression analysis where the cost level is explained by volume

• Assuming constant marginal cost, the regression coefficient will be an estimate of marginal cost

• Two types of analysis – OLS and Fixed Effects – which is the right one?

0

200000

400000

600000

800000

1000000

500 1500 2500 3500 4500

0

200000

400000

600000

800000

1000000

500 1500 2500 3500 4500

Shock analysis – Orkla/Cederroth

UiO April 13 201637

Close competitors?


Estimating diversion ratios using shock analysis

UiO April 13 201639

See paragraph 165 and 166 in decision V2015-30

𝐷𝑁𝑆𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑜𝑓𝑆𝑎𝑚𝑎𝑟𝑖𝑛

𝑟𝑒𝑑𝑢𝑐𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑜𝑓𝑁𝑦𝑐𝑜

Welfare standard – Egmont/CMore

UiO April 13 201640

Overlapping business between TV2 and C More

41

Sports

Pay-TV

Film andseries

Commercial channels

Film

Streaming

UiO April 13 2016

Tippeligaen and Premier League is not competing products

42

jan.

09

mar.

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mai.0

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TV 2 (Sport + Premium) C More (Total + Sport) TV2 + C More

• TL and PL had most subscribes at the time when TV2 controlled both rights

• Indicates that the non-competing rights are most efficiently used when the same player controls both set of rights

TV2-TL, C More PL TV2 TL & PL TV2 PL, C More TL

UiO April 13 2016

Efficiencies – TeliaSonera/Tele2

UiO April 13 201643

TeliaSonera gets approval of Tele2 acquisition in Norway

UiO April 13 201644

“I am pleased that the Norwegian Competition Authority sees the advantages with this transaction. This is good, not only for our and Tele2's customers, but

also for Norway as a whole. We will be a stronger and more credible alternative to Telenor on their home market. We will now further accelerate the roll-out of

mobile Internet”

- Johan Dennelind, President and CEO of TeliaSonera

Three types of efficiencies

UiO April 13 201645

1. Dynamic efficiencies – more customers increase the incentive to invest

– Increased quality and new products

– Closer to Telenor – more competition

2. Reduced variable cost – incentive to compete more aggressively on price

3. Lower fixed cost – able to maintain production level using less resources

Hvor store gevinster skal til?

UiO April 13 201646

• http://www.tu.no/artikler/teliasonera-kjoper-tele2/231087:

«The company expects synergies of at last 800 SEK from 2016.»

• How much need to be considered a gain to society?

– Simple calculation based on possible price increase, margin, elasticity of demand and market size

– Price increase of (p) 5%, margin (m) 50%, elastisity (e) -0,25 and a market of 15 mrd –dead weight loss of 100 mill.

– dead weight loss % 𝑜𝑓 𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟𝑒×𝑝2

2+𝑚 × 𝑝 × 𝑒

www.osloeconomics.no


Information and strategic interaction Assumptions of perfect competition: (i) agents (believe they) cannot influence the market

price (ii) agents have all relevant information What happens when neither (i) nor (ii) holds? Strategic interaction among a group of firms where some or all are incompletely informed In particular: What happens when a firm knows more than the others about demand, own costs, etc.? Equilibrium outcome is now also determined by incompletely informed firms’ beliefs. These beliefs are represented by subjective probabilities. (i) Incomplete information in a static model

- how beliefs determine the equilibrium

(ii) … in a dynamic model - how beliefs are formed


Games with incomplete information Perfect Bayesian Equilibrium: Both strategies and beliefs are in equilibrium. • Given the strategies in equilibrium, which revised beliefs

are consistent with these strategies? • Given the beliefs in equilibrium, which strategies are in

equilibrium? Two different kinds of problem: • Asymmetric information – and the importance of the

uninformed firm observing the informed firm’s actions. • Symmetric, incomplete information – and how there still

may be a lot of action even though firms cannot observe each other’s actions.

Signalling A typical signalling game: Stage 1: The informed player chooses an action (signals) Stage 2: The uninformed player observes stage 1, revises his beliefs about the informed player, and chooses an action himself. The informed player’s private information – his type

θ ∈ {High, Low}


The uninformed player’s beliefs about the other’s type: Initial beliefs Pr(High) = pH Pr(Low) = pL = 1 – pH Stage 2: revised beliefs Equilibrium: actions and revised beliefs Separating equilibrium: the action taken by the informed player at stage 1 depends on his type. Pooling equilibrium: the action taken by the informed player at stage 1 is independent of his type. In a pooling equilibrium, the uninformed player learns nothing about the other player’s type from observing his stage-1 action. Beliefs cannot be updated based on that action. In a separating equilibrium, on the other hand, the stage-1 action reveals the informed player’s type, and so, based on that action, the uninformed player can update his beliefs about the other player’s type and act accordingly.


First – a static model: Price competition with asymmetric information Two firms. Product differentiation. Price competition. Product differentiation: A slight increase in a firm’s price causes a slight decrease in its demand and a slight increase in the other firm’s demand. D1 = D1(p1, p2); D2 = D2(p2, p1)

− + – + Firm 1 has private information about own costs. Both firms know firm 2’s costs. Firm 1’s unit costs: c1 = Lc1 , with probability x

c1 = Hc1 , with probability (1 – x) Lc1 < Hc1

Firm 2 only knows the probability distribution (Lc1 , Hc1 , x) Firm 1 knows both c1 and the probability distribution.


In the case of complete information: π1 = (p1 – c1)D1(p1, p2)

( ) ( ) ( )0

,,

1

21111211

1

1 =∂

∂−+=∂∂

p

ppDcpppD

p

π

Best response of firm 1: R1(p2). Slope of the best response:

sign R1’(p2) = sign 21

12

pp ∂∂∂ π

.

( ) ( ) ( )

21

2112

112

211

21

12 ,,

pp

ppDcp

p

ppD

pp ∂∂∂−+

∂∂=

∂∂∂ π

• First term positive

• Slope of the best response positive unless 21

12

pp

D

∂∂∂

very

negative.


Equilibrium with complete information:

R2(p1)

R1(p2) p2

p1


The optimum p1 is increasing in c1:

0111

12

121

12

=∂∂

∂+∂∂

dccp

dpp

ππ

0211

211

211

2111

2

1

1 >∂∂∂∂=

∂∂∂∂∂−=

p

pD

p

cp

dc

dp

πππ

HR1

R2

LR1 p2

p1


Firm 2 doesn’t know firm 1’s type. Firm 2 behaves as if confronting an expected firm 1. Analytically, we find three prices:

The price of the uninformed firm. The price of the informed firm if it has high costs. The price of the informed firm if it has low costs.

eR1

*1Hp

*1Lp

p2*

HR1

R2

LR1 p2

p1


How is the equilibrium affected by incomplete information? If firm 1 is low-cost, then incomplete information increases the equilibrium prices. If firm 1 is high-cost, then incomplete information reduces the equilibrium prices. Probability of firm 1 being low-cost: x An increase in x reduces equilibrium prices, whether firm 1 is low-cost or high-cost. If firm 1 could choose x, it would want x to be low, whether the firm actually is low-cost or high-cost. • The informed firm would like to be believed to have high

costs, because that would keep prices high.


Dynamic model Stage 1: An action by firm 1 that may potentially influence firm 2’s subjective probability that firm 1 is low-cost. Stage 2: Price competition with asymmetric information What action? (i) Verifying costs – external audit

Verification is good for firm 1 if it is high-cost, but not if it is low-cost.

(ii) Verification not possible Model: Two-period price competition between two firms Period 1: Price competition Period 2: Price competition Is it possible for firm 2 to infer firm 1’s cost from firm 1’s price in stage 1? In period 1, a high-cost firm 1 would want to set a price that reveals its cost, while a low-cost firm 1 would not want to reveal its cost.


Signalling game. Could it be possible for a high-cost firm 1 to set a price in period 1 that is so high that a low-cost firm 1 would not want to mimic it? – Yes, because increasing the price is less costly for a high-cost firm than for a low-cost firm. π1 = (p1 – c1)D1(p1, p2)

01

1

11

12

>∂∂−=

∂∂∂

p

D

cp

π

The effect on firm 1’s profit of a price increase depends on the firm’s costs. The higher costs are, the stronger is the effect if it is positive, and the weaker is the effect if it is negative.

p1

π1

high-cost

low-cost


A separating equilibrium is one where firm 1’s price in period 1 depends on its costs. A pooling equilibrium is one where firm 1’s price in period 1 is the same whether it is low-cost or high-cost. If firm 1’s price in period 1 reveals its costs, then there is complete information in period 2. If firm 1’s price in period 1 is uninformative of its costs, then the period-2 game is as in the static model. Firm 1 would want firm 2 to believe it is high-cost, whether this is true or not.

R2

HR1 LR1 p2

p1


Firm 2 will only believe firm 1 is a high-cost firm if it sets a price in period 1 that is so high that a low-cost firm would never set it – even though, by doing so, it would be considered a high-cost firm in period 2. Thus, in a separating equilibrium, the high-cost best-response curve in period 1 is further to the right than in the static model. Therefore, the expected best-response curve shifts to the right, and all prices are higher in period 1 of the two-period model than in the static model. An extension: each firm has private information about own costs. The result that prices are higher still holds. [Mailath, ”Simultaneous Signaling in an Oligopoly Model”, Quart J Econ 1989]

High-cost firm sets high price today in order to induce a high price tomorrow. → Puppy Dog strategy

p2

p1


Entry deterrence Top Dog strategy Two periods. Firm 1 has private information about own costs. Period 1: Firm 1 is monopolist. It cannot deter entry through capacity investments, etc. Can it deter entry through its period-1 price? Firm 1 wants firm 2 to believe its costs are low.

01

2 >∂∂

c

π, 02 <

∂∂

x

Eπ

The interesting case: Entry is profitable for firm 2 if firm 1 has high costs but not if it has low costs. Reducing the price is less costly for a low-cost firm than for a high-cost firm.

p1

π1

high-cost

low-cost


Complete information: Period-1 price is the monopoly price. Firm 2 enters if and only if firm 1 has high costs. Incomplete information: One of two situations may occur. (i) Low-cost firm 1 sets a price below its monopoly

price, in order to signal its low costs. • Separating equilibrium

(ii) Both types of firm 1 set the low-cost monopoly

price. • Pooling equilibrium • Can only happen if firm 2, without any new

information, is deterred from entry. Limit pricing: Price reduction to deter entry. Is limit pricing credible? In case (i), it is. The price reduction in the separating equilibrium serves to inform the potential entrant that entry is not profitable because of the presence of a very potent incumbent. In case (ii), it is not. However, the outside firm hasn’t learned anything during period 1 and therefore chooses to stay out.


What are the welfare consequences of incomplete information? In both cases: Expected price lower because of incomplete information. In case (i) – separating equilibrium – entry behaviour is unaffected by incomplete information. Thus, with a separating equilibrium, incomplete information is good for welfare. In case (ii) – pooling equilibrium – the high-cost firm 1 manages to deter entry by mimicking the low-cost type. Thus, incomplete information implies less entry. Total effect on welfare is unclear. What if the entrant does not know its own costs? Suppose firms’ costs are the same, but only firm 1 knows what they are.

02 <∂

∂c

π

Firm 1 wants to signal high costs in order to deter entry. Now, the high-cost firm sets price above monopoly price in order to deter entry. Puppy Dog as entry deterrence. [Harrington, ”Limit Pricing When the Potential Entrant Is Uncertain of Its Cost Function”, Econometrica 1986]


Incomplete information and unobservable action • Rival’s price is unobservable

(recall Green & Porter)

• Incomplete information about demand • Symmetric information: Both firms incompletely

informed • Learning over time

- Collecting information today in order to have more knowledge about demand tomorrow

• Strategic aspects of learning

- A firm may try to disturb the other firm’s learning today in order to affect future decisions

Model: Two firms. Two periods. Product differentiation. Price competition each period.

- Prices are strategic complements. Firms do not observe each other’s prices. Firms do not know the market demand function.

qi = a – pi + bpj


• Firm A wants firm B to set a high price in period 2. • Firm B will only set a high price in period 2 if it believes

demand is high. • Firm B may think demand is high if it has high sales in

period 1. • Firm A may set a high price today in order for firm B to

believe demand is high. • But also firm B reasons the same way about firm A. • And each firm also knows the other firm manipulates its

learning. • Both firms set high prices in period 1 in order to

manipulate each other’s learning. • But each firm is able to see through the other firm’s

manipulation and learns the correct demand condition before period 2.

• Signal-jamming: manipulating others’ learning • In our case: signal-jamming increases period-1 prices.


Signal-jamming

� � �

termstochastic

firm by thecontrolled

other by theobserved

εα +=s

Other applications: Organizational economics, corporate governance

– moral hazard A specific model: Firms: I and II No costs. Demand: Di(pi, pj) = a – pi + pj, i ≠ j. No firm knows a, only its expected value: ae = Ea The one-period case: (Benchmark) Each firm solves:

( ){ } ( ) ijie

ijiip

pppapppaEEi

+−=+−=πmax

Best-response function: 2

je

i

pap

+=

Equilibrium: pI = pII = ae.


The two-period case: Learning about a if other firm’s price is observable: a = Di + pi – pj But other firm’s price is not observable

��

termstochastic

firmby controlled

firmby observed

appD

j

j

i

ii +=+��

In a symmetric equilibrium, each firm sets the same price in equilibrium, α, so that: Di = a – α + α = a But which price? If firm II sets the price α and believes firm I does the same, what price would firm I want to set? Firm II ’s estimate of a after period 1:

1~IIDa = = a – α + 1

Ip → ( )1~~Ipaa =

In period 2, firm II believes it is playing a game of complete information where a = ( )1~

Ipa .

→ ( )12 ~III pap =


What are the incentives for firm I to set a price in period 1 that differs from α? First, consider period 2: Firm I has been able to deduce the true a and solves:

( )[ ] 212 ~max2 IIIp

ppapaI

+−

→ ( )

222

~ 1112 αα −+=+−+=+= IIII

pa

paapaap

Firm I’s period-2 profit:

21

2

2

−+= απ II

pa

Period 1: What is the optimum price for firm I in period 1, given firm II ’s price α? Discount factor: δ ∈ (0, 1] Firm I solves:

( )

−+++−21

11

2max

1

αδα III

ap

pappaE

I


FOC: 02

21

1 =

−+++− αδα IeI

e papa

In a symmetric equilibrium: 1Ip = α. ae – 2α + α + δae = 0 ⇒ First-period price: α = ae(1 + δ) • Manipulation of learning fails. • The firms set higher prices in period 1 than if

manipulation of each other’s learning were not possible. • Puppy-dog strategy: A high price today in order for the

other firm to believe demand is high and therefore set a high price tomorrow.


Strategic interaction in one market – incomplete information in another A version of predation: The stronger firm competes aggressively in order to reduce the weaker firm’s financial resources.

Product market: Duopoly – complete information Capital market: Competitive – incomplete information Two periods. The two firms differ in financial strength: The “long purse” story. In order to operate in the market in period 2, each firm has to incur an investment K. Firm 1 has internal funds in excess of K. Firm 2 has to borrow on the capital market: Its internal funds equal E < K. Firm 2 borrows D = K – E, and has to pay back: D(1 + r) Interest rate: r


Firm 2’s gross profit in period 2 is stochastic: π~ ∈ [π,π ] Cumulative distribution function: F(π~); F’(π~) = f(π~) Expected value: πe

If π < D(1 + r), then firm 2 goes bankrupt. Bankruptcy: The bank receives π and incurs bankruptcy costs B. Competitive capital market – banks’ profits 0. Banks’ cost of funds: r0

The interest rate in equilibrium solves:

( ) ( )( )[ ] [ ] ( )( )

( )DrdfBrDFDrrD

0

1

1~~~111 +=−++−+ ∫+

ππππ

The expected bankruptcy costs will have to be covered by the borrowers. So firm 2’s capital costs is [(1 + r0)E] + [(1 + r0)D + BF(D(1 + r))] = (1 + r0)K + BF((K – E)(1 + r))


Firm 2’s expected net profit in period 2: W = πe – (1 + r0)K – BF((K – E)(1 + r)) The higher is firm 2’s internal funds, the more likely is it that firm 2 will undertake the period-2 investment: An increase in E

- lowers debt K – E - lowers interest rate r

Thus: 0>dE

dW

Period 1: • E is a function of firm 2’s period-1 profits. • Firm 1 can lower E by reducing prices in period 1. • Predatory pricing.


Research and development (R&D) What will a market look like in the future?

- which firms? - which products? - which production technology?

Depends on:

- entry deterrence, mergers, etc. - regulation - consumers’ preferences - innovation ← - …

Two kinds of innovation • Product innovation • Process innovation Product innovation a special case of process innovation?


Process innovation What is the value of an innovation?

- for society - for the innovating firm

It depends on the situation. Patents: protecting inventions Consider a firm making an innovation that is patent-protected forever. Constant unit costs. The innovation reduces costs from c to c, c > c. The value to a social planner

( )∫= c

cs dccD

rV

1

c D(p)


The private value (1) monopoly

π(p, c) = (p – c)D(p)

pm(c) = argmaxp π(p, c)

πm(c) = π(pm(c), c)

( ) ( )c

cp

cdc

dp

pdc

cd mmm

∂∂=

∂∂+

∂∂= ,ππππ

= – D(pm(c))

pm(c) > c, ∀ c ⇒ D(pm(c)) < D(c), ∀ c.

( )( ) sc

cmm VdccpD

rV <= ∫

1

Private value is less than social value


(2) competition Suppose all firms in the market have constant unit costs c . Homogeneous products. Price competition. p = .c π = 0. One firm makes an innovation, getting c = c. Two cases to consider: (i) The innovation is drastic: pm(c) ≤ c .

Even at the monopoly price, the innovating firm takes the whole market.

(ii) The innovation is non-drastic: pm(c) > c .

Also now, the innovating firm takes the whole market, but has to set p = c .


Consider a non-drastic innovation.

πc = (c – c)D(c )

( ) ( ) ( )∫=−= c

cc dccD

rcDcc

rV

11

∀ c > c, pm(c) > pm(c) > c ⇒ D(pm(c)) < D(c ), ∀ c > c. ⇒ Vm < Vc. D(c ) < D(c), ∀ c < c . ⇒ Vc < Vs ⇒ Vm < Vc < Vs

Exercise 10.1: This ranking also holds for drastic innovations


Why is Vm < Vc? The replacement effect of an innovation. (Arrow, 1962) In the competition case, the innovating firm escapes a zero-profit situation. In the monopoly case, the innovating firm replaces one monopoly situation with another one. Because of the replacement effect, competition is good for firms’ incentives to innovate. Exercises 10.2, 10.3.


(3) a monopolist threatened by entry Suppose the entrant innovates in case the monopolist does not. This increases the monopolist’s incentives to innovate, since now the alternative is worse. πd(c1, c2) – profit per period in a duopoly when own cost is c1 and rival’s cost is c2. If the monopolist does not innovate and the other firm enters and does innovate, then the monopolist earns πd(c , c) and the new firm earns πd(c, c ). Assumption: πm(c) ≥ πd(c , c) + πd(c, c ) Value of the innovation for the monopolist:

Vm = r

1[πm(c) – πd(c , c)]

⇒ Vm – Vc = r

1[πm(c) – πd(c , c) – πd(c, c )] ≥ 0

Opposite ranking, because of the efficiency effect: a monopolist earns more than two duopolists.


The two effects:

- the replacement effect

- the efficiency effect

Patent race

Two firms, incumbent and potential entrant, fight to be first to make an innovation with an ever-lasting patent.

The more valuable the innovation is for the incumbent, the more resources it spends on being first, and the greater is the probability that it will win the race and get even more control over the market.

If the efficiency effect dominates the replacement effect, then Vm > Vc and the incumbent gets even more control over the market.

Opposite, if Vc > Vm, then the entrant takes over, at least in expectation.

Tirole, Sec. 10.2


Strategic technology adoption Technology without patent protection. Technology adoption is costly. Two firms, homogeneous products. Constant unit costs c . Zero profits. Low-cost technology is available: c < c Non-drastic innovation: If only one firm adopts the new technology, then it earns c – c per unit per period. Assume: D(c ) = 1.

Value of innovation: V = r

cc −

Value for non-innovating firm: 0. Costs of adoption ⇒ A firm will not want to adopt if the other one has already adopted. Strategic incentives to adopt early. But what happens when both know they both have such incentives? Adoption costs are decreasing over time: C(t),

C(0) very high, C’( t) < 0, C’’( t) > 0.


Net present value of adopting new technology at time t, given that none of the firms adopted before time t, is: L(t) = [V – C(t)]e-rt This is the value of being technology leader. The follower does not adopt: F(t) = 0, ∀ t. (i) The technology leader picked in advance –

technology adoption without strategic considerations.

The leader maximizes L(t):

( ) ( ) ( )[ ] 0''

delay fromcost marginal

delay fromgain marginal

=

−−−= −rtetCVrtCtL��

C(t*) = V + ( )r

tC *' < V

(ii) Strategic considerations Both firms consider technology adoption Define tc by: L(tc) = 0 ⇒ C(tc) = V ⇒ tc < t*


A firm never adopts before tc. The best response to the other firm’s adoption at t’ > tc is to adopt at t ∈ (tc, t’). The best response to the other firm’s adoption at tc is not to adopt at all. The best response to the other firm not adopting is to adopt at t* > tc. The only possible equilibrium is one in mixed strategies. At each point t, each firm has a subjective probability p(t) that the other firm adopts the technology at t, given that none of the firms has adopted so far. In equilibrium, the firms are indifferent between adopting and not at each t ≥ tc. Payoff to each firm if they both adopt at time t:

B(t) = – C(t)e-rt Equilibrium condition: L(t)[1 – p(t)] + B(t)p(t) = F(t) [V – C(t)][1 – p(t)] – C(t)p(t) = 0

⇒ p(t) = 1 – ( )

V

tC, t ≥ tc

• A strong strategic incentive for adoption • But what if profits are positive with competition?

- product differentiation?


Network externalities Positive externalities between consumers Example: telephone, telefax More generally: network effects Example: system goods, such as

- computers / software, - DVD players / DVDs

When a new technology is available, each consumer must decide whether to switch. A coordination problem: the more consumers switching, the higher is the utility for each from switching. Excess inertia: consumers wait longer than what is socially optimum because no-one wants to be first to switch to the new technology. Excess momentum: consumers switch too early because they do not want to be left with the old technology. On the supply side:

- which technology to offer? - standardization of new technology - compatibility with other products


A model of consumer behaviour with network externalities Two consumers. Two technologies: old and new. q = network size ∈ {1, 2} u(q) = a consumer’s utility with old technology v(q) = a consumer’s utility with new technology Positive network externalities: u(2) > u(1), v(2) > v(1) Better to be together than separate: u(2) > v(1), v(2) > u(1)

Consumer 2 New Old

Consumer 1 New v(2), v(2) v(1), u(1) Old u(1), v(1) u(2), u(2)

Two pure-strategy equilibria: {New, New} and {Old, Old}. Excess inertia: If the consumers play {Old, Old} and v(2) > u(2). Excess momentum: If the consumers play {New, New} and v(2) < u(2).


A more sophisticated model Dynamic analysis: Two periods. Incomplete information about the other consumer’s preferences. A consumer of type θ has preferences

uθ(q) and vθ(q), q ∈ {1, 2}, θ ∈ [0, 1]. The higher θ is, the more interested the consumer is in switching to new technology:

( ) ( )[ ]

012 >−

θθθ

d

uvd

Network externalities: uθ(2) > uθ(1), ∀ θ; vθ(2) > vθ(1), ∀ θ. The highest θ-type prefers switching even if he is alone: v1(2) > v1(1) > u1(2) > u1(1) The lowest θ-type is the opposite: u0(2) > u0(1) > v0(2) > v0(1) • Coordination problems only for consumer types in the

middle range. Consumers are independently and uniformly distributed on [0,1].


Four possible strategies for a consumer: (1) Never switch (2) Do not switch in period 1; switch in period 2

regardless of what happened in period 1. (3) Do not switch in period 1; switch in period 2 if and

only if the other consumer switched in period 1. (4) Switch in period 1. Strategy (2) is dominated by strategy (4).

• Strategy (4) never fares worse than (2), and if the opponent plays strategy (3), then strategy (4) is strictly better than (2).

Equilibrium play depends on θ: 0 θ* θ** 1 A consumer of type θ* is indifferent between the old technology with a small network and the new technology with a big network: uθ*(1) = vθ*(2)

θ never (1)

jump on the bandwagon

(3)

immediately (4)


A consumer of type θ** is indifferent between: (a) switching to a big network only if the other consumer

switched in period 1, and otherwise staying in a big network; and

(b) switching in period 1, implying being in a small network if the other consumer plays strategy (1) and in a big network otherwise

vθ** (2)(1 – θ**) + uθ** (2)θ** = vθ** (1)θ* + vθ** (2)(1 – θ*) ⇔ [vθ** (2) – uθ** (2)]θ** = [ vθ** (2) – vθ** (1)]θ* ⇒ vθ** (2) > uθ** (2) Excess inertia may occur: In the case where both consumers have θs just below θ**, no-one switches to the new technology because they play the jump-on-the bandwagon strategy, even if vθ(2) > uθ(2). The supply side Stage 1: Each firm decides whether its product is to be compatible with rival firms’ products. Stage 2: Price or quantity competition. Trade-off: Compatibility implies a larger market, but tougher competition.


Vertical relations Products are sold through retailers. How does this affect market performance? pw – wholesale price

p – retail price Demand: q = D(p)

Contracts producer-retailer One extreme: vertical integration – producer and retailer act as if they are one firm The other extreme: linear price – total price is T(q) = pwq

p

pw

c

Producer

Retailer


Two-part tariff total price is T(q) = A + pwq price per unit decreasing in q – quantity discount A – franchise fee Resale price maintenance Producer determines the retail price. US Supreme Court: The Leegin case (2007) Variations: price ceiling, price floor. Exclusive dealing Retailer is not allowed to carry competing producers’ products. (inter-brand competition) Exclusive territories Retailer has the sole right to sell the producer’s products within a specified area. (intra-brand competition) Arguments for vertical integration • the theory of the firm – Ronald Coase • transaction costs • incentives for relationship-specific investments • we focus here on other arguments


Vertical externalities • Double marginalization If both producer and retailer are monopolists, then quantity sold is less than if they were integrated. pw > c ⇒ pm(pw) > pm(c) Example: D(p) = 1 – p, c < 1 (i) No integration The retailer solves: maxp πr = (p – pw)(1 – p)

2

1 wpp

+=⇒ 2

1 wpq

−=⇒

The producer solves:

( )2

1max w

wpp

pcp

w

−−=π

2

1 cpw

+=⇒ 4

1 ,

43 c

qc

p−=+=⇒

Total profit: ( ) ( ) ( )2

22

1163

161

81

ccc

rpni −=−+−=+= πππ


(ii) Integration The integrated firm solves: maxp πi = (p – c)(1 – p)

2

1 ,

43

21 c

qcc

p−=+<+=⇒

Profit: ( ) nii c ππ >−= 2141

Both the two firms and society would gain from integration. Alternatives to full integration (a) two-part tariff T(q) = A + pwq

The producer can set: pw = c, ( )

41 2c

A−=

Interpretation: Sell the whole business to the retailer for a price equal to monopoly profit – the retailer becomes the residual claimant. But: - risk-sharing: what if D(p) is uncertain and the retailer is

risk averse? - asymmetric information about D(p)


(b) resale price maintenance Producer restricts retail price: p ≤ pm, sets wholesale price: pw = pm. But again: risk sharing Other externalities - retailer service The retailer may, by putting in promotion effort, increase the demand for the product. But some of the increase in demand will benefit the producer. Two-part tariff still works (but: risk sharing?) Resale-price maintenance is not sufficient:

The producer would want to control the service level, too.

- input substitution

Tie-in: producer sells both inputs to the retailer.


A horizontal externality Several retailers. One retailer’s advertising effort benefits also the other retailers. The producer needs to encourage such efforts in order himself to benefit from this externality. Two-part tariff with pw < c Retailer power What if the retailer has the bargaining power? Example: the Norwegian grocery industry. Gabrielsen & Sørgard, “Discount Chains and Brand Policy”, Scandinavian Journal of Economics 1999. Johansen & Nilssen, “The Economics of Retailing Formats: Competition versus Bargaining”, Journal of Industrial Economics 2016.


Vertical foreclosure • A firm has control over the production of a product or

service that is an essential input for producers in a potentially competitive industry. The competition in this industry can be altered by the firm by denying or limiting access to the input.

• Essential facility

- bottleneck - network industries: firms need access to network to

deliver product or service � telecom: AT&T, Telenor � power: Statnett � shipping: harbours � railway: Eurotunnel

- outside network industries: firms are at a disadvantage without access

� computer reservation systems for airlines � cooperatives: ski lifts, newspapers, ATMs � distribution of goods: retailing chains (food

stores, pharmacies, book stores, pubs)

• Horizontal foreclosure: bundling, tying - complement products with one firm having (near)

monopoly in one of the markets - Microsoft

� Windows/internet browser � Windows/media player


The Chicago School • There’s only one monopoly profit to be had. • Vertical integration and vertical foreclosure cannot be

harmful. • If there is a problem, it is that there is no competition

upstream. The foreclosure doctrine The upstream firm does indeed have incentives to favour one downstream firm, such as a downstream subsidiary.

Upstream monopolist

Downstream subsidiary

Downstream competitor


A reconciliation: the role of commitment • Having contracted with one downstream firm, the

upstream firm has incentives to contract further with other downstream firms, even though these firms in turn will compete with the first firm and decrease its profit.

• The first downstream firm realizes this and is less willing

to sign a contract. This reduces the upstream firm’s profit.

• The upstream firm will be looking for ways to get around

this problem. → Vertical foreclosure • Analogue: The durable-good monopolist. (Ronald

Coase) Model

U

D1 D2

Consumers p = P(q)


Timing Stage 1: Firm U offers firms D1 and D2 tariffs T1(⋅) and T2(⋅) for purchase of the intermediary good. Each Di then orders a quantity qi and pays Ti(qi). Stage 2: Firms D1 and D2 transform intermediate good into final good and sell at price p = P(q1 + q2). Define: Qm = arg maxq {[ P(q) – c)]q}

pm = P(Qm), πm = (pm – c)Qm

Observable contracts Firm U offers (qi, Ti) = (Qm/2, pmQm/2) to each downstream firm. They both accept and sell in total monopoly quantity at monopoly price. No rationale for foreclosure. But can firm U commit to these contracts? • If U and D2 agree on (q2, T2) = (Qm/2, pmQm/2), then

firms U and D1 would want to sign a contract that maximizes their joint profit given the U/D2 contract, with a quantity q1 given by:

q1 = arg maxq {[ P(Qm/2 + q) – c)]q} > Qm/2.

• Anticipating this, firm D2 would turn down the (Qm/2, pmQm/2) offer.


Secret contracts Passive beliefs: If a firm receives an unexpected offer, it does not revise its beliefs about the offer made to its rival. Consider a candidate equilibrium in which firm Dj is offered a quantity qj. Whatever firm Di is offered, it still believes that firm Dj is offered qj. Firm U offers firm Di a quantity qi so that the joint profit for U/Di is maximized, given the offer of qj to firm Dj: qi = arg maxq {[ P(q + qj) – c]q} This is the same problem as the one facing a Cournot duopolist. q1 = q2 = qC – the Cournot quantity The profit of the upstream firm: πU = 2πC < πm • The upstream firm suffers from its inability to commit. • The problem becomes more severe the larger the number

of downstream firms. • The more competitive the downstream industry, the more

interested is the upstream bottleneck owner in foreclosure in order to retain profit.


Why does the upstream firm foreclose access? Not in order to extend its market power to the downstream market, but rather in order to re-establish the market power lost because of its inability to commit. Downward integration Firm U buys one of the downstream firms. It credibly offers the monopoly quantity Qm to its own affiliate and nothing to the other. Bypass: Sometimes, there is an alternative supplier available to the non-integrated firm, so that the foreclosing firm can be bypassed. Still, if the alternative supplier is less efficient – for example, has higher production costs c > c – foreclosure with bypass is inefficient. Exclusive dealing • By entering an exclusive-dealing contract with D1, firm

U commits itself not to supply to D2. • A substitute for vertical integration.


Auctions Auction:

• One seller and a small number of potential buyers

The mirror image – Contract auction / Procurement auction:

• One buyer and a small number of potential sellers. • The buyer decides on the purchasing procedure,

potential sellers bid their prices. When are auctions used? • A unique object

- well defined? indivisible? • Uncertainty about who should get the object / the

contract • Uncertainty about the object’s value / the project costs • Commitment to selling / buying procedure


Alternatives to auctions Market

- decides who gets the object / project - but how to determine the price?

Bargaining

- determines the price - but how to determine who is the counterpart?

Handing out for free

- beauty contest - lobbying costs

Two concerns with an auction • For society - efficiency: Is the object bought by the

bidder with the highest willingness to pay? • For the seller: Is the price the highest possible? Several auction procedures How are these questions affected by the procedure chosen?


Various kinds of auctions • Sealed bids vs. open bids • Open bids

- Ascending bids – English auction � bidders submit higher and higher bids until

only one bidder remains � art, collectibles

- Descending bids – Dutch auction � seller starts with a high price and cries out

lower and lower prices until a bidder accepts � flowers (Netherlands), fish (Israel), tobacco

(Canada) • Sealed bids

- First price:

� The bidder with the highest bid wins and pays his bid.

� real estate, government procurement

- Second price: � The bidder with the highest bid wins and pays

an amount equal to the second highest bid. � Vickrey auction [Vickrey, J Finance 1961]

- William Vickrey, Nobel laureate 1996

� stamps etc. [Lucking-Reiley, J Econ Perspectives 2000]


Basic model • Bidders are risk neutral • Bidders’ valuations are different but independent • Each bidder knows only his own valuation • Seller doesn’t know any bidder’s valuation • No observable differences among the bidders • Reservation price?


Bidder behaviour (i) English auction

- continuing bidding is profitable as long as own valuation > current high bid

- this strategy is independent of what other bidders do (dominant strategy)

- the winner is the one with highest valuation → efficiency

- price is (just above) second highest evaluation


(ii) Sealed-bid second-price auction bidder B’s valuation = v bidder B’s bid = b largest bid from others = a • With a valuation of v, what should be bidder B’s bid, b? Distinguish between two cases: a > v: B’s decision does not matter a < v: B wins if b > a, and earns (v – a) • Bidding b < v reduces B’s chances to win but does not

affect what he has to pay if he wins. • Optimum bid: b = v

(dominant strategy) • The winner is the one with highest valuation

→ Efficiency • The price equals second-highest valuation • English auction and sealed-bid second-price auction are

equivalent with respect to winner and price. • Contract auction:

- winner is the one with lowest cost - price equals second-lowest cost

• Calculating the bid is easy


(iii) Sealed-bid first-price auction • Bidder trades off two concerns:

Bidding b < v - reduces his chances to win; not good. - reduces the price he has to pay if he wins; good.

• This trade-off makes the optimum bid lower than v. • The bidder knows that other bidders think the same way:

All bidders bid below their valuation. This makes the optimum bid even lower.

• This also holds for (iv) Dutch auction • The winner is the one with the highest valuation • The price equals highest bid, which is lower than highest

valuation • Expected price = Expected second-highest valuation • Calculating bid is difficult


Equilibrium bid – sealed-bid first-price auction n bidders, vi ∈ [vl, vh], i ∈ {1, …, n} cumulative distribution function: F(vi), i ∈ {1, …, n} Let’s focus on a symmetric equilibrium. Bidders are not identical, since valuations differ. But there are no observable differences, so their valuations are all drawn from the same cdf. In a symmetric equilibrium, there exists some function B(v), which is the same for all players, so that if one’s valuation is v, the equilibrium bid is B(v). Consider bidder i. He does not know the other bidders’ vs but believes that their bids depend on their valuations according to the function B(v). Assume: B’ > 0. ⇒ A bid of b implies a valuation equal to B-1(b). The probability that i’s bid bi is the winning bid =

[F(B-1(bi))]n – 1

Bidder i’s expected profit: πi = [vi – bi][F(B-1(bi))]

n – 1


Optimum bid satisfies: 0=∂∂

i

i

b

π

=∂∂=

∂∂+

∂∂=⇒

i

i

i

i

i

i

i

i

i

i

vdv

db

bvdv

d ππππ [F(B-1(bi))]

n – 1

In a symmetric equilibrium: bi = B(vi), ∀ i. ⇒ vi = B-1(bi)

In equilibrium, bidders’ beliefs about each other’s valuations are correct.

( )[ ] 1−=⇒ ni

i

i vFdv

dπ

Assume (reasonably): πi = 0 if vi = vl. ⇒ B(vl) = vl.

Integration:

( ) ( )[ ]∫−=

i

l

v

v

ni dxxFv 1π

Two expressions for bidder i’s profit – must be equal.

πi = [vi – bi][F(B-1(bi))]n – 1 = ( )[ ]∫

−i

l

v

v

n dxxF 1

( )( )[ ]( )[ ] 1

1

−

−∫

−==⇒ n

i

v

v

n

iiivF

dxxFvbvB

i

l


Common for all four kinds of auctions (in the base model):

• Efficiency: Object to the bidder with highest valuation (or lowest cost)

• Revenue equivalence: All four kinds give the seller the

same expected income. • An increase in the number of bidders increases the

expected price. - the more bidders, the higher is the expected second-

highest valuation. Difference among the auctions: • Bid more difficult to calculate in sealed-bid first-price

and Dutch auctions than in sealed-bid second-price and English auction.


Seller’s reservation price Revenue equivalence in the basic model: Seller indifferent between auction procedures. But what about a reservation price? A parallel situation: The monopolist’s problem A monopolist trades off two concerns: • wants to sell large quantities → low price • wants to earn a profit per unit sold → high price Optimum trade-off: Price above marginal cost Auction: Seller trades off the same two concerns: • wants to sell the object → low reservation price • wants to earn a profit if the object is sold

→ high reservation price The two highest valuations: v1, v2 Reservation price: r Three cases: (i) v1 > v2 > r: increasing r has no effect (ii) v1 > r > v2: increasing r increases the price (iii) r > v1 > v2: increasing r reduces the chances to sell


Optimum reservation price with 1 bidder Bid = r or nothing Seller’s own valuation: v0 Seller’s expected profit: π(r) = r[1 – F(r)] + v0F(r) FOC: [1 – F(r)] – rf(r) + v0f(r) = 0

⇒ ( )

( ) ( )rJrf

rFrv ≡−−= 1

0

i.e., marginal cost = marginal revenue ⇒ r = J-1(v0) Generally: If highest bidder has valuation v, his expected gain is

( )

( )vf

vF−1

so that the expected price in this case is

( )

( ) ( )vJvf

vFv =−− 1

The seller sells only if J(v) ≥ v0 for the highest bid ⇒ r = J-1(v0)

Effiency with a reservation price: • With a reservation price, the object may not be sold,

even if a bidder exists with v > v0. • Ex-ante efficiency vs. ex-post efficiency.


Some extensions (i) Observable differences among the bidders

Example: Public procurement – domestic vs. foreign firms. Suppose foreign firms are more cost effective than domestic ones.

• English auction and sealed-bid second-price auction are

still efficient. • Sealed-bid first-price auction no longer efficient: it is

possible to win the auction without having the lowest cost.

• It is optimum for the procurer to discriminate between

bidder groups, and one is no longer certain that the project is won by the lowest-cost bidder.

• In the example: It is optimum to discriminate in favour

of the domestic firms. This favouring - increases the chance of getting an inefficient

supplier, but also - lowers the bid from the efficient firms


(ii) Risk-averse bidders • In a sealed-bid first-price auction, risk-averse bidders bid

higher than risk-neutral ones. An increase in the bid (1) increases the chance of winning, and therefore

getting something (2) reduces what one earns in case of winning.

With risk aversion, (1) gets more important than (2) • Contract auction: Risk averse bidders bid more

aggressively than risk neutral bidders. • The seller gains more in a sealed-bid first-price auction

than in a sealed-bid second-price auction.

(iii) Correlated valuations • Extreme case: identical valuations. Bidders do not know

the object’s true value but have access to different pieces of information about this value. No bidder knows what other bidders know.

• More common in auctions than in contract auctions?

Auctions: - buying for resale - exclusive rights Contract auction - pioneering projects with great cost uncertainty for all potential suppliers


• “Winner’s curse”

- Bidders base bids in a sealed-bid auction on estimates. The bidder with the most optimistic estimate wins.

- If you win, then you will wish to revise your estimate: The winner is the most optimistic one.

- But this is taken into consideration in the bids: Bids are even lower because of the “winner’s curse”.

• In an English auction, bidders learn from each other

during the bidding process. This reduces the winner’s-curse problem.

- With correlated values, an English auction is preferred by the seller to the other kinds.

• Asymmetric information

- one bidder knows the object’s true value - US offshore oil and gas lease auctions

- Porter, Econometrica 1995


Other issues • Collusion

- second-price auction better for sustaining collusion among bidders than first-price auction

- open bids better than closed bids - contract auctions: Norsk Standard

• divisible objects

- securities, quotas • combined bids

- petroleum: price on exploration right + production fee

- vague projects: price + content • entry costs, number of bidders, participation fee • auctioning incentive contracts • competition for a market vs. competition in a market


Efficiency of auctions • Which auction procedure to use?

- revenue equivalence - easily calculated bids

→ sealed-bid second-price auction But: risk aversion? correlated values? • Which objects are sold most effectively in an auction?

- unique object - uncertainty about willingness to pay:

how large? who? • Does price affect efficiency?

- one unit – no quantity effects from price change - divisible objects (quotas, securities): quantity

effects Repeated auctions

- Less aggressive bidding today in order not to reveal one’s high valuation before future auctions (the ”ratchet” effect)

- better to have large projects? negotiating renewal with current supplier?

- Capacity constraints: The winner of a contract today may not have capacity to participate in the next round.

Documents

Strategic competition - Forsiden · Tore Nilssen – Strategic Competition – Theme 1 – Slide 4 Even in the study of a single industry, it may be helpful to have different models