Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
Lecture 23Oligopoly, Cournot and Stackelberg
Competition
Econ 301Professor S. Severinov
UBC
Oligopoly – Characteristics
Small number of firms Product differentiation may or may not exist Barriers to entry Each Firm affects the price and the total quantity in the market Each firm’s action depends on the actions of the other
firms
Oligopoly – Equilibrium
If one firm decides to change their quantity or cut their price, they must consider what the other firms in the industry will do Could cut price some, the same amount, or more
than firm Could lead to price war and drastic fall in profits
for all Actions and reactions are dynamic, evolving over
time
Oligopoly – Equilibrium
Defining Equilibrium Firms are doing the best they can and have no incentive to
change their output or price All firms assume competitors are taking rival decisions into
account Nash Equilibrium
Each firm is doing the best it can given what its competitors are doing
We will focus on duopoly Markets in which two firms compete
Oligopoly: Cournot Model
Different modes of competition in real world call for different models of behavior
The Cournot Model: Oligopoly model in which firms produce a homogeneous good, all firms decide simultaneously how much to produce each firm treats the output of its competitors as
fixed and chooses its best response to it.
Firm will adjust its output based on what it thinks the other firm will produce
Slide 6
Oligopoly- Duopoly The market for movies in a medium size city Dixon:
Sony’s Loews Theatres and local Main Street Movies (MSM) are the only two players.
The demand for movies: P=12 – Q.
P is the price of a ticket (in $).
Q is number of seats (in ‘000) demanded per week.
The marginal cost of offering movie shows for each firm is not important, what matters is that both firms have identical and sufficiently small marginal costs which we set to 0.
Loews and MSM have to make capacity choices (in thousands of seats) for theatres to build.
Slide 7
Duopoly: Loews & MSM Let us solve for Nash equilibrium when capacity choices
are made simultaneously (i.e. when making its capacity choice, a firm does not
observe its rival’s capacity).
MSM’s capacity qM ; Loews’ capacity qL.
Zero costs: this assumption is for simplicity, so that we can focus on strategic, not technological factors.
Nash equilibrium q*M and q*L must be best responses to each other:q*M maximizes MSM’s profits when Loews chooses q*L.
q*L maximizes Loews’ profits when MSM chooses q*M.
Slide 8
Duopoly: Loews & MSM Profit Functions of MSM and Loews are:
Nash equilibrium: every firm is at its best response to the rival’s action.
First Step: compute best responses:€
P rM = P ×q M = 1 2 −q M −q L( )×q M
P rL = P ×q L = 1 2 −q M −q L( )×q L
€
q M* m a x i m i z e s
P r M = 1 2 − q M − q L*( )q M = 1 2 q M − q M
2 − q L* q M
q L* m a x i m i z e s
P r L = 1 2 − q M* − q L( )q L = 1 2 q L − q L
2 − q M* q L
Slide 9
Loews & MSM To maximize PrM take its derivative with respect to qM
and set it equal to zero. This would give qM*. Using the General Rule 1, we have:
Set this to zero:
So, the best response function of MSM is:
*212PrLM
M
M qqdq
d −−=
0*212 * =−− LM qq
26
** LM
qq −=
Slide 10
Loews & MSM Repeating the same steps to maximize PrL gives us
the best response of Loews
Recall that MSM’s best response function is:
Solving these two equations in two unknowns gives you the equilibrium quantities:
Profits are: P×q=16 (thousand) for each firm.
2q6q
*M*
L −=
2q6q
*L*
M −=
4qq-12 = P
4qq *L
*M
*L
*M
=−
==
Oligopoly: Graphical Representation
The Reaction Curve The relationship between a firm’s profit-
maximizing output and the amount it thinks its competitor will produce
A firm’s profit-maximizing output is a decreasing schedule of the expected output of Firm 2
Firm 2’s ReactionCurve Q*2(Q1)
Reaction Curves and Cournot Equilibrium
qM
qL
6 12
12
Firm 1’s ReactionCurve Q*1(Q2)
6
x
x
x
In Cournot equilibrium, eachfirm correctly assumes how
much its competitors willproduce and thereby
maximizes its own profits.
CournotEquilibrium
Firm 1’s reaction curve shows how much itwill produce as a function of how much it thinks Firm 2 will produce. The x’s
correspond to the previous model.
Firm 2’s reaction curve shows how much itwill produce as a function of how much
it thinks Firm 1 will produce.
Cournot Equilibrium
Cournot equilibrium is an example of a Nash equilibrium (Cournot-Nash Equilibrium)
Each firm’s reaction curve tells it how much to produce given the output of its competitor
Equilibrium in the Cournot model, in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly
Cournot Equilibrium
Q1
Q2
Firm 2’sReaction Curve
12
6
Firm 1’sReaction Curve
6
12
4
4
Cournot Equilibrium
The demand curve is P = 12 - Q andboth firms have 0 marginal cost.
Firm 1’sReaction Curve
Firm 2’sReaction Curve
Duopoly ExampleQ1
Q2
12
12
4
4
Cournot Equilibrium
CollusionCurve
3
3
Collusive Equilibrium
For the firm, collusion is the bestoutcome followed by the Cournot
Equilibrium and then the competitive equilibrium
6
6
Competitive Equilibrium (P = MC; Profit = 0)
Slide 16
For comparison, consider a monopoly: If Loews and MSM are to collude and act as a single
firm splitting profits in half they will choose q to maximize:
The monopoly price would be P=12-6=6Monopoly profits: 6*6=36If firms will split them equally each will earn 18
( )
60212
i.e. 0,MR :iscondition order -First
1212Pr 2
==−
=
−=−=
qqqqMonop
Profit Maximization w/ Collusion
Collusion (contract) Curve q1 + q2 = 6
Shows all pairs of output q1 and q2 that maximize total profits
For example: q1 = q2 = 3 Less output and higher profits than the Cournot
equilibrium
Conclusion: there is an incentive to collude and split the marketBut is collusion going to be sustainable?
Competition Versus Collusion:The Prisoners’ Dilemma Cournot Nash equilibrium is a noncooperative
equilibrium: each firm makes decision that gives greatest profit, given actions of competitors
Although collusion is illegal, why don’t firms cooperate without explicitly colluding? Why not set profit maximizing collusion price and
hope others follow?
Collusion Game: Payoff Matrix
MSM
Loews
Choose q=3 Choose q=4
Choose q=3
Choose q=4
$18, $18 $15, $20
$16, $16$20, $15
Non-sustainability of Collusion
If the firms try to collude, it will not be sustainable, Will not be a Nash equilibrium Each Firm would like to deviate from the collusive
agreement to produce 3 and produce more (say 4) thereby increasing profits unilaterally.
In fact, best response to q=3 is q=6-3/2=4.5
Slide 21
First-Mover advantage
When one firm chooses its action before competitors (due to faster reaction, earlier investment, history factors,
patents), it gets an opportunity for strategic commitment.
How would that affect the outcome of competition? Naturally, this depends on the market, the nature of the
product, etc.
First Mover Advantage – The Stackelberg Model Oligopoly model in which one firm sets its output
before other firms do Assumptions One firm can set output first MC = 0 Market demand is P = 12 - Q where Q is total
output (as in the Cournot Case)
Slide 23
Stackelberg Model: Sequential Moves
Suppose that Loews gets to choose its capacity first.
MSM will observe Loews’ capacity and choose its capacity second.
Very Important: Loews predicts how MSM will react - it uses ‘look forward and reason back approach.’
MSM’s best response (from above) is:
2q6q L*
M −=
Slide 24
Stackelberg Game: Sequential Moves
Given MSM’s best response function, Loews understands that if it chooses a quantity qL, MSM will respond by choosing
So, Loews’ profits from choosing some qL would be
( ) LL
LLL
LLMLL q
2q6q q)
2q6(12q qq12Pr
−=
−−−=−−=
2q6q L
M −=
Slide 25
Sequential Moves To find Loews’ optimal choice as a leader, maximize
Take the derivative of PrLL
Setting it to zero gives us optimal choice of Loews as a leader qL
*= 6. MSM as a follower will then choose
LL
LL q6
qPr −=
dd
2qq6q
2q6Pr
2L
LLLL
L −=
−=
32
q6q*
L*M =−=
Slide 26
Sequential Moves
With qL*=6K and qM *=3K, price is P=12-qL*-qM
*=$3 Profits are:PrL= $18,000PrM= $9,000
Recall that under simultaneous moves, each firm chooses quantity 4K and earns 16K in profits.
So, the first mover benefits. But the second-mover loses. Question: Why does L raise its quantity?
Slide 27
When does the first mover have an advantage?
Strategic behavior produces different outcomes depending on the order of moves.
It is often an advantage to move first, but whether there is such an advantage depend on the nature of the environment.
What are the features of markets and products where the first mover has an advantage and where it does not?
What about R&D: is it better or worse to move first?
Slide 28
First-Mover Advantage
First-mover advantage is not acquired by luck.
It comes from costly commitments made earlier: product positioning decisions taken in the past, R&D, early investments, smart contracting strategy.
Pursuing the first-mover advantage is risky:If demand is low, an early investment may be lost
Slide 29
First-mover advantage and the airline industry
Air Canada and WestJet are the two main carriers on the Vancouver-Toronto route. They both also serve many other routes in Canada and US.
Capacity decisions in the airline industry take the form of buying or leasing airplanes.
Is AC or WJ likely to be able to secure the kind of first-mover advantage on the Vancouver-Toronto route that Loews was seen to achieve in. Why or why not?