The effects of Partial Cross-Ownership on competition

The effects of Partial Cross-Ownership on competition

May 2009

Denisse Halm | anr. 702025

Bachelor Thesis International Economics & Finance

Supervisor: Prof. Dr. W. Mueller

Word Count: 7898

2 | Partial Cross-Ownership

Table of ContentsTable of ContentsTable of ContentsTable of Contents

Table of Contents .......................................................................................................................................... 2

Introduction .................................................................................................................................................. 4

Chapter 1: Literature Review ........................................................................................................................ 6

Reynolds and Snapp (1986) The competitive effects of partial equity interests and joint ventures ........ 6

Flath (1991) When is it rational for firms to acquire silent interests in rivals? ......................................... 8

Malueg (1992) Collusive behaviour and partial cross ownership of rivals ................................................ 9

Alley (1997) Partial ownership arrangements and collusion in the automobile industry ....................... 11

Dietzenbacher et al. (1999) Horizontal integration in the Dutch financial sector .................................. 13

Chapter 2: Cournot competition with shareholding ................................................................................... 15

General Case ........................................................................................................................................... 15

Duopoly Case .......................................................................................................................................... 16

Symmetric Case ....................................................................................................................................... 17

Chapter 3: Bertrand competition with shareholding .................................................................................. 19

General Case ........................................................................................................................................... 19

Duopoly Case .......................................................................................................................................... 20

Symmetric Case ....................................................................................................................................... 21

Chapter 4: An application ........................................................................................................................... 22

Introduction ............................................................................................................................................ 22

The model ............................................................................................................................................... 23

No distinction between countries ....................................................................................................... 23

Distinction between countries ............................................................................................................ 23

Operating Profits ................................................................................................................................. 24

Cournot competition ........................................................................................................................... 24

Results from empirical research ............................................................................................................. 25

Chapter 5: Competitive Analysis ................................................................................................................. 29

Collusion .................................................................................................................................................. 29

Regulatory instruments .......................................................................................................................... 33

EC Merger Regulation ......................................................................................................................... 33

Article 81 EC ........................................................................................................................................ 34

Partial Cross-Ownership | 3

Article 82 EC ........................................................................................................................................ 34

Conclusion ................................................................................................................................................... 36

Appendix ..................................................................................................................................................... 37

Cournot Competition .............................................................................................................................. 37

No-ownership Cournot ....................................................................................................................... 37

General Cournot .................................................................................................................................. 37

Duopoly Cournot ................................................................................................................................. 38

Symmetric Case ................................................................................................................................... 39

Bertrand Competition ............................................................................................................................. 39

No-ownership Bertrand ...................................................................................................................... 39

No-ownership Bertrand ...................................................................................................................... 40

General Bertrand ................................................................................................................................ 40

Bertrand duopoly ................................................................................................................................ 41

Symmetric Bertrand ............................................................................................................................ 43

Application .............................................................................................................................................. 44

Bibliography ................................................................................................................................................ 45


IntroductionIntroductionIntroductionIntroduction

Partial cross-ownership (from now on PCO) is the practise of firms acquiring some shares in one or

more of their rivals in an industry.1 This alters the profit function the companies face, since they now

maximize their operating earnings jointly with their earnings from the PCO arrangements. Suspicion of

collusive behaviour arises easily from this matter. Surprisingly though, it is only slightly regulated by

competition authorities both in the European Union and in the United States.

Research in this field has been done recently by economists and some law experts, some investigate

it from a theoretical perspective like Reynolds and Snapp (1986) and Malueg (1992), and others base

their research on specific industry cases, such as in Amundsen and Bergman (2002) and Dietzenbacher

et al. (1999). Gilo et al. (2004) identify three different types of PCO schemes: unilateral cases, where one

firm acquires shares in one of its rivals, e.g. the acquisition by Microsoft of shares in Apple; multilateral

cases, where several firms in an industry acquire shares in one or more of its competing companies,

these type of arrangements have been studied in previous papers, such as the case of the Japanese and

American automobile industry (Alley, 1997); and the case when a dominant shareholder makes passive

investments in rival firms, for example Ford’s acquisition of silent share interests in Budget Rent a Car

(Purohit & Staelin, 1994).

Furthermore, the terminology used when investigating PCO differs according to the author. In this

paper, however, it is all incorporated without distinction. More specifically, when referring to a PCO

arrangement or scheme, it might also be called shareholding. Most of the papers which are dealt with

here, take shareholding to be passive, also named silent, that is, when one firm acquires interests in

another, these are non-voting shares, and therefore give no control to the shareholding firm,

irrespective of the shares’ size. Finally, a controller is a firm’s major shareholder, who usually makes the

output or price choice.

The objective of this thesis is to clarify the effects PCO has on the industry output and price levels,

and its effect on competition, to determine whether the current regulation is sufficient for the

competition concerns it raises. The first chapter reviews some of the previous literature. The works

chosen give a summary of the research from different perspectives. The thesis continues with the

modelling of PCO in a Cournot setting in Chapter 2, and in a Bertrand setting in Chapter 3. An application

1 PCO can also take the shape of vertical shareholding, however, it is not the subject of this paper.


of the quantity competition model is presented in Chapter 4. Chapter 5 presents the perspectives on

collusion under price competition and shows the findings of Ezrachi and Gilo (2006) regarding the

applicability of the policy instruments in the EU to the phenomenon of PCO. The paper ends by

presenting the conclusions.


Chapter 1: Chapter 1: Chapter 1: Chapter 1: Literature ReviewLiterature ReviewLiterature ReviewLiterature Review

Several economists have contributed to the analysis of PCO by developing different models. In this

chapter, some of the works by these authors are reviewed by presenting the setting, the models and

conclusions they drew. The papers chosen cover the research of PCO from different perspectives: a

general model, the Cournot and Bertrand competition models, the possible effects on collusion, and

some applications of these models to different industries.

Reynolds and Snapp (1986) The competitive effects of partial equity interests and joint

ventures

This paper looks at the gains from efficiency given by the PCO structure, such as joint R&D funding

and technology sharing, and the loss in competition that arises from it. (Reynolds & Snapp, The

competitive effects of partial equity interests and joint venture, 1986, p. 142) A market is studied where

n firms compete in quantities with constant marginal costs, c, and entry is not possible.

When firms engage in PCO, it is always the controller of each firm that decides the level of output to

be produced by the firm. Since the profit function of a typical firm i in this market includes the earnings

it makes from its own production plus the dividends it receives from its ownership of shares in rivals,

each firm’s profits do not only depend on the output choice made by its own controller, but it also

depends on the choice made by the rival firms in the industry. The profit function of firm i is:

k

ik

k

iki

ik

k

kii qcpvqcpv )()(1 −+−

−=Π ∑∑

≠≠

where kiv is the share firm k (each of the other firms in the industry) owns in firm i, ikv is the share firm i

owns in each of the other firms k, p is the market demand, iq is the output of firm i, and kq the output

of each firm k ≠ i.

When choosing its optimal output level, firm i maximizes its profit function with respect to firm i’s

quantity iq :


0)(10: =∂

∂+

∂

∂+−

−⇒=

∂

Π∂∑∑

≠≠

k

i

ik

k

iki

i

ik

k

ki

i

i qq

pvq

q

pcpv

qFOC

After rearranging, the best response function is found:

k

ki

i

iV

qV

qp

pcq

−−

∂∂

−=

1

where kV is the sum of all shares all of the rival firms owns in firm i. The authors do not specifically

mention the form of the shares ikv that firm i owns in each of its competitors, but since it is factored

out as iV , where ∑≠

=ik

k

iki vV , it has to be implicitly assumed that they are equal for all firms.

From the last equation above, the effect of PCO on output is examined. The authors find that an

increase from either side, i.e. firm i increases its ownership in another firm or another firm k increases

its ownership of firm i, decreases the optimal output level. The decrease in output in turn increases

prices to a level higher than that under the ‘normal’ Cournot equilibrium without ownership ties.2

Intuitively, when firm i owns shares in its competitors, it takes part of the rivals’ profits for itself. By

choosing a lower quantity, firm i increases its total profit, which includes its operating earnings and the

profit it makes through shareholding. In this sense, under PCO, firms set a quantity that is lower than the

Nash equilibrium without PCO, and closer to the collusive outcome.

In the appendix the authors study the special case of symmetry between all firms. Shares are set

equal, kiik vvv == , and are at its maximum level n

v 1= . Demand for the product is linear. The first

order condition derived above is adjusted for this specific case so that the optimal output level in the

symmetric case is found:

p

qpcqn

qq

p

n

nq

q

pcp

n

n

qFOC

i

i

∂

∂−=

=∂

∂−+

∂

∂+−

−−⇒=

∂

Π∂

)(

01

)(1

10:

2 The No-Ownership scenario is computed in the Appendix


Since Qqn = , where Q is total industry output, is the monopoly output level, it is concluded that given

this setting, all firms jointly produce the monopolistic outcome, regardless of the number of firms in the

industry. Given the pro-collusive aspect of this result, the perspectives on collusion are investigated.

In industries where PCO arrangements exist, collusion is more likely to be sustained since there is a

reduction in the gains a firm experiences when it deviates. When a firm deviates, it hurts its competitors’

profits, and therefore, the share of those that the deviating firm would earn itself. For this reason, the

higher one firm’s interests are in another, the lower the first one’s incentives to cheat. It becomes clear

that in the presence of PCO possible cartel profits are enhanced.

In conclusion, the linking of profits between competitors specified by the PCO structure in a given

industry alters the optimal level of output chosen by each firm. Specifically, these levels tend to be lower,

the higher the shareholding interests between firms in the market.

Flath (1991) When is it rational for firms to acquire silent interests in rivals?

In this paper, PCO is modelled as a two stage game where n=2. In the first stage, the share trading

subgame, firms acquire shares in its competitor’s firm. While in the second stage (the product market

subgame), firms choose output quantities or prices. A key assumption for this model to be valid is that

‘share prices reflect a correct anticipation of the product market equilibrium’. (Flath, When is it rational

for firms to acquire silent interests in rivals? 1991, p. 573) In other words, a firm will only acquire shares

in its rival if it knows that the firm it is buying shares of has made a profit in the previous periods and will

therefore increase the acquirer’s own profit in the next period.

The model is solved by backwards induction: first, the product market subgame is solved. PCO

arrangements are taken as given, and the optimal output and price combination is determined. Then,

the second stage is solved. The firm’s payoff function, which includes its operating profits, its profits

from shareholding and the cost of acquiring shares, is maximized with respect to the share interest it

owns in other firms to find the optimal level of share acquisition.

The author finds that whether acquiring shares is a subgame perfect Nash equilibrium, i.e. there is a

Nash equilibrium in each stage of the game, depends on whether the control variables in the product


market subgame are strategic substitutes or strategic complements. (Flath, When is it rational for firms

to acquire silent interests in rivals? 1991, p. 577)

According to Church and Ware (2000), under Cournot competition, quantities are strategic

substitutes: if firm 1 increases its output quantity, the natural response of firm 2 will be to reduce its

own quantity. Conversely, under Bertrand competition, prices are strategic complements. If firm 2

chooses a higher price, firm one will respond by also increasing its price.

Flath (1991) found that only if the control variables are strategic complements, is share acquisition

the subgame perfect outcome. Given this result, the author examines the cases of Cournot and Bertrand

competition individually.

In the Cournot setting, the control variables are the quantities, which are strategic substitutes. It is

therefore the case that under Cournot competition, share acquisition cannot be subgame perfect. (Flath,

When is it rational for firms to acquire silent interests in rivals? 1991, pp. 578-579) In this sense, this

game can be seen as a prisoner’s dilemma, i.e. share acquisition is not a subgame perfect solution, even

though it is in the best combined interest of both firms to establish a PCO agreement.

In the case of Bertrand competition, with the control variables being prices and therefore strategic

complements, share trading is subgame perfect.

Malueg (1992) Collusive behaviour and partial cross ownership of rivals

In this paper, the effects of PCO on collusion are investigated in an industry where competition

happens in quantities. The setting is a symmetric duopoly where cross-ownership shares are always

equal to v, with [ )2

1;0∈v and marginal costs are assumed to be zero for both firms. The static

equilibrium consists of each firm maximizing its single period profits:

( )211

1 vpqpqv +−=Π

where 1Π is the profit of firm 1 and ( )x

Qp −= 1 is the demand function both firms face with

21qqQ += and 0>x . Firm 1 maximizes its profit with respect to its quantity, obtaining the Cournot

equilibrium:


( )( ) ( )

( ) ( ) ( )[ ] ( )

( )xv

vq

qQvxQqQxvq

FOC

qQvqQv

n

xxx

xx

+−

−=

=−−−+−−−⇒=∂

Π∂

−+−−=Π

−−

)1(2

1

0111)(10:

111

2

1

1

1

1

1

211

The collusive outcome is achieved when both firms jointly produce the monopoly output level. In the

first order condition above, 02

=q :

( )xq

m

+=

12

1

Finally, a deviating firm would produce:

( )( )2112

321

xv

vvxxq

d

+−

−−+=

In order to study the repeated game and in it collusion, the author chooses x=2 from now on. Profits

in each of the three cases above are the following:

,)2(2

13

v

vn

−

−=Π ,

27

2=Π m .

)1(1458

)45(2

3

v

vd

−

−=Π

Malueg’s result is consistent with that of Reynolds and Snapp (1986). The higher the levels of PCO

among firms, the closer the deviating profit is to the monopoly profit. Therefore, the incentives to

deviate become smaller. Also, since the Cournot profit increases the higher the degree of PCO, the

punishment after deviation becomes softer. With these results in mind, the author examines collusion in

the repeated game.

Collusion is studied in a setting where an infinite repetition of the above static game takes place. The

author finds the minimum discount rate that would sustain collusion in the repeated scenario:

( )333

233

)1(729)2()45(

)1(108)45()2(

vvv

vvvnd

mdC

−−−−

−−−−=

Π−Π

Π−Π≡δ


The author finds that the discount factor,Cδ , decreases until the shares reach the level 304.0=v ,

and then increases. Therefore, it can be said that for the higher levels of PCO, i.e. 5.0304.0 << v , an

increase in v will make collusion harder to be sustained. In other words, when the level of cross-

shareholding is very high, it is more difficult for firms to collude than under ‘normal’ (no ownership)

competition.

Alley (1997) Partial ownership arrangements and collusion in the automobile industry

This paper presents the case of the Japanese and American automobile industries and how PCO

affects its structure. Japanese firms are known to be part of PCO webs between firms, the so-called

keiretsus. For this reason, it would be rational to think that these industries should be characterized by

high levels of collusion. The author finds the level of collusion in the Japanese and American automobile

industries, both of which are characterized by different PCO structures, and compares them.

About these structures it is important to note that not only are there significant (silent) interests

between Japanese car manufacturers, but it is also the case that American firms own shares in Japanese

ones. The author finds that possible reasons behind the acquisition of shares in rival firms in the

automobile industry (within and across borders) are the possibilities to gain insight into the competitors’

technology and expertise. Interestingly, the author points out that with PCO, firms ‘gain many of the

benefits of a merger while still retaining their autonomy.’ (Alley, Partial Ownership Arrangements and

Collusion in the Automobile Industry, 1997, p. 193)

The PCO arrangements in this industry are modelled with conjectural variations where N firms

produce a homogenous good, under the assumption that all shareholding is silent. The profit function

for firm i looks as follows:

[ ] [ ]∑∑≠≠

−−+−−

−=Π

ij

jjjjjiiiii

ij

iji FxcpxsFxcpxs )()(1

where ijs are the shares of firms j owned by firm i, p is the demand function, ix is the quantity of the

good produced by firm i, )( ii xc are the variable costs of production, and iF are the fixed costs firm i


faces. A conjectural variations parameter α which measures the degree of collusion in the industry is

integrated. It is characterized by [ ]1;1−∈α and by ( )ijij xxxx // α=∂∂ for all j ≠ i. From the parameter,

the following industries features can be determined:

• When 0>α : collusion is taking place in the market, its degree is highest when the parameter is

closest to 1.

• When 1=α : the industry is a perfect cartel.

• When 0=α : the industry is shaped by Cournot competition

• When 1−=α : firms compete à la Bertrand (without fixed costs)

When maximizing the profit function with respect to quantities, it becomes clear that the price-cost

margin depends directly on the shares firms hold in one another. Therefore, the author states that given

PCO exist in the industry, not accounting for it in the profit function would be mistaken, since it would

yield a biased estimate of α.

Moreover, the model is extended to implement trade. It is expected that both domestic markets, i.e.

the American and the Japanese, should become more competitive, due to the increase in the number of

firms competing in each market. The profit function of firm i now looks as follows:

[ ] [ ]∑∑≠≠

−+−++−+−+

−=Π

ij

j

e

j

d

jj

e

j

ed

j

d

jii

e

i

d

ii

e

i

ed

i

d

ij

ij

T

i FxxcxpxpsFxxcxpxps )()(1

where the superscripts d and e relate to the domestic and export quantities and prices.

There are now three conjectural variation parameters: ( )d

i

d

j

d

i

d

j xxxx // α=∂ measures

competition between domestic producers, ( )d

i

md

i

mxXxX ∂∂=∂∂ // β estimates the degree of

competition between domestic producers and importing firms, and ( )e

i

e

j

e

i

e

j xxxx // γ=∂∂ shows how

competition works between exporting companies.

The model derived above is used in the third part of the paper to estimate the conjectural variations

parameters. The dataset includes data for 11 Japanese and 3 American car manufacturers collected over

15 years. It is found that with the inclusion of trade, imports have a negative effect on price-cost

margins, whereas exports have a relatively small but positive effect on these. The estimation yields


α=0.2183 and γ=0.0201 suggesting that collusion does take place in the Japanese domestic market, but

it does not occur in the export market. These results are similar to the case when PCO arrangements are

not present.

Finally, for the sake of comparison, the author estimates the values for the American market without

exports. After comparing the results, he finds that imports have opposite effects on the price-cost

margins in the two markets.

Concluding, the author finds evidence that collusion does indeed happen in the Japanese domestic

market, but not in the export market. Surprisingly, he also finds that collusion is stronger in the

American market than in the initially suspected Japanese market. (Alley, Partial Ownership

Arrangements and Collusion in the Automobile Industry, 1997, p. 202)

Dietzenbacher et al. (1999) Horizontal integration in the Dutch financial sector

In this paper, the authors extend the model by Flath (1991) and investigate PCO arrangements in the

Dutch financial sector. First, a general model is developed, which is then studied in the cases of price

and quantity competition.

The profit function of firm i is presented in its general form:

∑≠

Π+−=Πij

jijiiii dqcp )(

where ip is the price charged by firm i, ic the firm’s unit cost of production, iq the quantity produced

by firm i, and ijd are the shares of firm j owned by firm i. The profit of firm i consists of two parts, its

own operating earnings and its earnings from shareholding in rivals, which can be direct (firm i earns

dividends from firm j) or indirect (firm i earns dividends from firm j, which in turn earns dividends from

firm k; without firm i having shares in firm k). As a consequence it happens that total profits in the

industry exceed total operating earnings in the industry. This is explained by ‘double counting’ due to

shareholding.

Next, the profit function above is used to study the Cournot competition case, where n symmetric

firms produce a homogenous good. It is found that the effects of PCO on the operating earnings of a


firm are so strong that a firm might even choose to stop producing altogether if its profits from

shareholding in rivals (when it does not produce itself) exceed the ones from its own production.

(Dietzenbacher, Smid, & Volkerink, Horizontal integration in the Dutch financial sector, 2000, p. 1229).

When Bertrand competition is considered, n firms have asymmetric unit costs and produce a

heterogeneous good. The authors conclude that with shareholding, the lower bound for the price-cost

margin is the monopolist’s, implying that under PCO, firms can minimally gain the monopolist’s margin.

Given that costs do not change, this means that with PCO firms competing à la Bertrand can profitably

raise prices above the monopoly level.

Finally, the model is applied to the Dutch financial sector, where banks compete either in the price

they charge for their services (deposit accounts, insurance policies) or in the quantities they ‘produce’ of

these. Given that the industry is characterized by a small number of large firms, the dataset includes 97

banks, three of which jointly hold between 70 and 80 percent of the market share depending on the

type of service. These firms are ABN Amro, Rabobank, and ING. This industry drew the authors’

attention since the data showed a decrease in competition brought about by wider margins and thus

higher profits between the year 1984 and 1991. Also, it is important to note that in the Netherlands,

banks and insurance companies are not allowed to merge, for this reason they operate under the same

holding company.

In the paper, competition has been looked at from both perspectives: price and quantity competition.

In the latter case, the authors found that ‘The effect of shareholding is a 1.37% increase of the price.’

(Dietzenbacher, Smid, & Volkerink, Horizontal integration in the Dutch financial sector, 2000, p. 1235)

And that price-cost margins increased by at least 8 percent. Also, output shares under PCO differ

significantly from those expected under the no-ownership Cournot scenario. When looking at price

competition, there was a clear need to use differentiated goods for this industry, since the costs of

banking and insurance differ considerably. It is found that the price-elasticities of AEGON, ING, and

Fortis are three to four times larger than those of ABN Amro and Rabobank. Also, it is clear that

shareholding increases the price-cost margins of firms involved in shareholding at least by two percent,

when price competition is considered.


Chapter 2: Cournot competition with shareholdingChapter 2: Cournot competition with shareholdingChapter 2: Cournot competition with shareholdingChapter 2: Cournot competition with shareholding

In this first study, the effects of PCO are investigated by looking at an extended model of a Cournot

oligopoly which incorporates PCO. Three cases are presented: first, the very general case is developed

for an industry with n possibly asymmetric firms with unit costs ic . Secondly, the model is solved for a

Cournot duopoly, again with asymmetric firms. Finally, the model presents a symmetric oligopoly with n

competitors.3

General Case

This model deals with the most general case. The industry is characterized by n competitors

producing a homogenous good that faces an unspecified demand P . Each firm has the following profit

function:

∑∑≠≠

−+−−=Πn

ij

jjijii

n

ij

jii qcPvqcPv )())(1(

where jiv is the share each of the firms j in the market own in firm i, for all ij ≠ and conversely,

ijv is

the shares firm i possesses in every firm j for all ij ≠ , iq is the quantity chosen by firm i.

The profit function consists of two parts: the company’s operating earnings represented by the first

term on the right hand side of the equation, and the earnings it makes from shareholding, the second

term.

Maximizing the profit function with respect to the output quantity iq yields:

0)1(0: =∂

∂+

−+

∂

∂−⇒=

∂

Π∂∑∑

≠≠

n

ii

j

i

ijii

i

n

ij

ji

i

i qq

PvcPq

q

Pv

qFOC

After rearranging, the best response function of each firm looks as follows:

3 For the all step-wise developments of the models in this chapter, refer to the Appendix.


)1( j

n

ii

jij

i

ii

V

qv

qP

Pcq

−−

∂∂

−=

∑≠

where ∑≠

=n

ij

jij vV .

When comparing the best response function above with the best response in the No Ownership

scenario developed in the Appendix, it is clear that in an industry where competition takes the form of

quantities, in the presence of PCO arrangements, the optimal output quantity of each firm is lower. In

other words, when firms hold silent interests in each other, they will always choose to produce a lower

amount than they would under normal competition.

The result above is similar to that concluded by Reynolds and Snapp (1986). Nevertheless, they differ

in one aspect: here firms are assumed to be completely asymmetric, i.e. they face different unit costs of

production and own different amounts of shares in each other. In Reynolds and Snapp (1986) firms are

asymmetric, yet, the authors sum all shares ijv to iV , and therefore implicitly assume that these are

equal among all firms. Put differently, the authors assume that the amount of shares firm i owns in firm j

is equal to the amount firm i possesses in firm k or firm j owns in firm s. This is not assumed in the result

stated above.

Following basic microeconomics, it can be concluded from the demand function, that the lower the

quantities produced by all companies, the higher the price they will charge for the product, and in turn,

the higher their realized profits.

Duopoly Case

It is now assumed that n = 2, and firms still face an unspecified demand function P , hold asymmetric

shares in one another, and face asymmetric costs of production. The result above is adapted to the

duopoly case. Two best response functions follow:


)1(

)1(

12

121

2

22

21

212

1

1

1

v

qv

qP

Pcq

v

qv

qP

Pcq

−−

∂∂

−=

−−

∂∂

−=

In order to find the solution, i.e. the output choices of each firm, the above system of equations is

solved by substitution. The optimal output choices of firms 1 and 2 given the shares they own in each

other are:

( )

( )

2112

21

1

121

2112

1221

2

2

2

1221

12

2

212

1221

2112

1

1

1

1

1*

1

)1)(1(*

1

1*

1

)1)(1(*

vv

v

qP

cPv

vv

vv

qP

Pcq

vv

v

qP

cPv

vv

vv

qP

Pcq

−−

−

∂∂

−+

−−

−−

∂∂

−=

−−

−

∂∂

−+

−−

−−

∂∂

−=

Again in this case, there is a clear dependence of the optimal output quantities of each firm on the

shares both firm hold in one another. More specifically, the higher the level of cross-ownership among

the two competitors, the lower their output choices will be. Once more, the price of the product is

negatively related to the quantity produced.

This model is a generalization of that studied by Malueg (1992), where firms here are not symmetric

in costs of shares.

Symmetric Case

Finally a symmetric case is considered. Firms are assumed to have equal unit costs and equal

shareholding, therefore they produce the same quantities. Demand for the homogenous product

produced by the n firms in the industry is still unspecified. The following holds:

vvv jiij == with [ )nv /1;0∈

ccc ji ==

qqq ji ==


Once again, the result from the general case above is adapted according to the assumptions just

discussed. The best response function, assuming firms are symmetric, makes:

)1(* vnv

qP

Pcq +−

∂∂

−=

Even though this case is highly unrealistic, it has been studied previously in, for example, Malueg

(1992) in the case of a duopoly. Due to the complexity of the asymmetric model, the symmetric case

was used by the author mention to investigate collusion in industries characterized by PCO. As

mentioned in Chapter 1, Reynolds and Snapp (1986) also explore this example. They examine the case

where symmetric shares are set to its maximum. They find that ‘given the number of firms in the market,

the monopoly output level will result regardless of the number of firms.’ (Reynolds & Snapp, The

competitive effects of partial equity interests and joint venture, 1986, p. 147)


Chapter 3: Bertrand competition with shareholdingChapter 3: Bertrand competition with shareholdingChapter 3: Bertrand competition with shareholdingChapter 3: Bertrand competition with shareholding

In this chapter, the effect of PCO will be examined in an industry where firms compete in price rather

than quantities. The structure of the chapter is symmetrical to that of Chapter 2.

General Case

In this general representation of price competition, n firms produce a heterogeneous good at a unit

cost ic which is different for every producer. Each firm’s profit function looks as follows:

∑∑≠≠

−+−−=Πn

ij

jjjijiii

n

ij

jii qcpvqcpv )())(1(

where jiv

is the share each firms j in the market own in firm i, for all ij ≠ and

ijv is the shares firm i

possesses in every firm j for all ij ≠ , iq is the quantity produced by firm i, and ip is the price charged

by firm i. As in the Cournot case, the profit function consists of two parts: the firm’s own operating

earnings and its earnings from shareholding in rivals. The assumption that firms produce a

heterogeneous good is important, since otherwise the firm charging the lowest price (approaching ic )

would take the whole market and earn monopoly profits.

Maximizing firm i’s profit with respect to the price it charges yields:

0)()()1(0: =−∂

∂+

−

∂

∂+−⇒=

∂

Π∂∑∑

≠≠

n

ij

jj

i

j

ijii

i

ii

n

ij

ji

i

i cpp

qvcp

p

qqv

pFOC

After rearranging, the best response function of firm i to the prices chosen by all other firms j in the

industry is:

i

ij

n

ij

jji

jij

i

i

i

i

i

pq

V

cpp

qv

c

pq

qp

∂∂

−

−∂

∂

−+

∂∂

−=

∑≠

)1(

)(


where ∑≠

=n

ij

jij vV .

Comparing the above result to the No Ownership case in the Appendix, it is clear that price is directly

affected by shareholding. In the best response function, this effect arises from the last term on the right

hand side of the equation. Surprisingly, the best response function decreases with PCO.

Duopoly Case

The model above is now solved for when there are only two producers in the industry. Due to the

complexity of solving the Bertrand competition model generally, in this case, two assumptions are made:

first, both firms will be symmetric in costs, and these will be zero for simplicity. Secondly, the demand

function is assumed to be:

jii ppq γ+−= 1

where iq is the quantity produced by firm i, ip is the price it charges for the product, and jp is the

price firms i’s competitor chooses. The parameter γ with the property [ ]1;0∈γ measures how

substitutable the products of each firm are. The more substitutable two products are, the more their

prices will affect the quantities produced by the firms.

The result from the general case above is changed to incorporate the two assumptions. Once

rearranged, it yields the following best response function:

)1(22

1

ji

jijj

iv

pvpp

−+

+=

γγ

The model is solved for a duopoly by substitution. The chosen prices for firm 1 and firm 2, given their

shares in each other’s companies are:


( )( )))(1()1)(1(4)1(

1)1()1()1(2

))(1()1)(1(4

)1()1)(1(2

2

1221

2

211212

2

212112121221

2

12

2

2

1221

2

2112

2

122112212112

1

vvvvv

vvvvvvvp

vvvv

vvvvvvp

−−−−−−

−+−−+−−=

−−−−−

−+−+−−=

γ

γ

γ

γ

From the solution above, it can be concluded that in the presence of PCO in a Bertrand duopoly

setting, firm’s price choices are complexly dependent on the shares each firm holds in one another.

Symmetric Case

Finally, the case where all firms are equal in costs ccc ji == and shares vvv jiij == is examined.

Once more, the demand function takes the specific form:

jii ppq γ+−= 1

The solution for this case with n firms is:

( )( ) γ

γ

−−−

−−−−+−−=

vn

vnvncvnp

)1(12

)1()1(1)1(1

As expected, the higher the level of PCO, as measured by the shares, the lower the equilibrium price.

A curious remark from the formula above is that the number of firms in the industry only plays a role in

the determination of the equilibrium price when there is cross-shareholding. Without PCO, i.e. setting

0=v , the optimum price is:

γ−

+=

2

1 cp


Chapter 4: An applicationChapter 4: An applicationChapter 4: An applicationChapter 4: An application

In this chapter, the Cournot model presented in Chapter 2 is applied to a market. The paper by

Amundsen and Bergman (2002) is interesting to study, since it takes the quantity competition model

developed in its general form and applies it to the electricity market in Norway and Sweden. In addition,

it is extended to include trade.

This chapter begins with an introduction to the situation in the Nordic electricity market, then

continues with the presentation of the model without distinction between counties, to later make that

distinction. The composition of the operating profits of each firm is explained. Next the model is laid out

for quantity competition including trade between countries. Finally the results from the empirical

research by the authors are presented.

Introduction

The Swedish electricity market was characterized by its high concentration, HHI = 0.3 according to

Amundsen and Bergman (2002). In 1996, in an attempt to deregulate the industry, it was suggested that

Vattenfall, the state owned firm with the highest market share, should split, so as to weaken its market

power. However, instead of splitting the firm, the government engaged in the integration of the

electricity markets among the Nordic countries. According to Amundsen and Bergman (2002, p. 74), ‘as

the degree of concentration was much lower in Finland and Norway [...] integration across the national

borders seemed to be an efficient way of diluting market power in Sweden.’ The process started by

integrating the Swedish and Norwegian markets in 1996, with Finland joining two years later, and

Denmark finally integrating in 2000. This resulted in several mergers and acquisitions across borders,

both horizontal and vertical.

With the integration of these markets, consumers experienced a decrease in prices at first, to only

later, once the integration process was completed, see a sharp increase in these. Given the facts, the

authors investigate whether the acquisition of shares between competitors in the market for energy

generation did not bring back the market power that existed before the integration of the Nordic power

market. (Amundsen & Bergman, Will Cross-Ownership Re-Establish Market Power in the Nordic Power

Market. 2002, p. 74)


For this purpose, a model is studied where big firms compete in the generation of electricity à la

Cournot, and the small ones are assumed to be price takers. The model only includes Norway and

Sweden, and only considers the high demand seasons for electricity: autumn, winter, and spring. The

authors state that the reasons for firms to acquire silent shares in its competitors according to von der

Fehr, et al. (2002) are the expected synergies in costs, the financial considerations, such as asset

management, and learning. These reasons confirm the statement by Alley (1997) mentioned in the first

chapter, that firms obtain most of the benefits from a merger just by acquiring passive shares in its rivals,

and still keep their independence in price and quantity setting, even though these may be influenced

through shareholding.

The model4

No distinction between countries

Each firm’s value consists of two parts: its own operating profits iΠ and its earnings from the shares

it holds in its rivals:

∑∑≠≠

+Π−=N

ij

jiji

N

ij

jii VvvV )1(

where N is the total number of firms in Norway and Sweden, ijv is the share firm i owns in firm j, and

jV is the value of firm j which again include firm j’s own operating profits and the earnings from the

ownership in other firms k.

Distinction between countries

The value of firm i in country C is:

C

CC

CCC

CC

CCC j

N

ij

jii

N

ij

iji vvV Π+Π−= ∑∑≠≠

)1(

4 The nomenclature of the variables used in the model presented here, do not correspond to those in the original paper. They

have been changed in accordance with the ones used in the previous chapters.


where Ci is the subscript identifying firm i in country C with },{ NSC ∈ , country C being either Sweden

or Norway. Finally, N , the total number of firms, is the sum of firms in the both countries

NS NNN += .

Operating Profits

The operating profits of firm i from country C comprise the profit it earns from the quantity it

produces and sells in country C plus the quantity it produces in country C and exports to country R with

CR ≠ :

RCRCCCCRCCCC

RCRCCRCCCCCCC

RCCCC

iRCiiiiRiCi

iRCiiiRiiiCi

iii

qqqCqPqP

qqCqPqCqP

;;;;;

;;;;;

;;

;

;

)(

)()(

ϕ

ϕ

−+−+=Π

−−+−=Π

Π+Π=Π

where CP is the price of electricity in country C, RP is the price of electricity in country R,

CCiq

,

is the

quantity firm i produces and sells in country C, RCi

q,

is the quantity firm i produces in country C and sells

in country R, )(;; RCCCC iii qqC + is the unit cost of producing in country C, regardless of where the product

is sold (the cost function is, for simplicity, assumed to be linear here) , and RC ;

ϕ is the unit cost of cross-

border transmission of electricity from country C to country R.

Cournot competition

When deciding on the quantity to be produced, firm i from country C maximizes its total value Ci

V :

( )

( )RCRCCCCRCCC

CC

CC

RCRCCCCRCCC

CC

CCC

jRCjjjjRjC

N

ij

ji

iRCiiiiRiC

N

ij

iji

qqqCqPqPv

qqqCqPqPvV

;;;;;

;;;;;

;

;

)(

)()1(

ϕ

ϕ

−+−++

−+−+−=

∑

∑

≠

≠

Firm i has to make two choices: how much to produce to sell at home CCi

q;

, and how much to

produce to sell abroad RCi

q;

. With this in mind, two first order conditions are derived:


0)1(0:

0)1(0:

;

;

;

;;

;

;

;

;;

;2

1

=

∂

∂+

−−+

∂

∂−⇒=

∂

∂

=

∂

∂+

−+

∂

∂−⇒=

∂

∂

∑∑

∑∑

≠≠

≠≠

RC

RCCC

CCCRC

RCCC

CC

RC

C

CC

CCCC

CCCCC

CCCC

CC

CC

C

j

i

RN

ij

jiRCiRi

i

RN

ij

ij

i

i

j

i

CN

ij

jiiCi

i

CN

ij

ij

i

i

qq

PvCPq

q

Pv

q

VFOC

qq

PvCPq

q

Pv

q

VFOC

ϕ

After rearranging, the best response functions for firm i from country C are:

∑

∑

∑

∑

≠

≠

≠

≠

−

−

∂∂

+−=

−

−

∂∂

−=

N

ij

ij

j

N

ij

ji

i

R

RCRi

i

N

ij

ij

j

N

ij

ji

i

C

Ci

i

CC

CC

RC

CC

CC

RC

C

RC

CC

CC

CC

CC

CC

CC

C

CC

v

qv

qP

PCq

v

qv

qP

PCq

)1(

)1(

;

;

;

;

;

;

;ϕ

It is clear that the quantity chosen by firm i to sell at home is symmetric to the result obtained in

Chapter 2. The fact that firm i owns shares in its competitors, will lead it to choose a lower output

quantity at home than under normal circumstances. The second result is of the same form as the one

above, but it includes the cost of transmission. This is straightforward, the amount of energy a firm

chooses to produce for export will not only depend on the demand it faces where it will be sold, but also

on the costs of producing and transporting it. Also here is shareholding of great importance. The higher

the shares firm i from country C has in firm j from the same country (with both countries exporting to R),

the lower the quantity firm i will choose to produce and export to R.

Results from empirical research

The model presented above was used to simulate the Swedish and Norwegian electricity markets. It

is important to note that these markets are characterized for having a few big firms and some smaller

ones, which are summarized into a group called ‘Competitive Fringe’. The distribution of firms in the

industry depending on their installed capacity of production looks as follows:


Table 1: Installed Capacity (MW) of NOR and SK Power producers (1999)5

Further, the web of PCO between Swedish and Norwegian firms is presented below:

Table 2: Partial Ownership Structure in NOR and SK in 1999 (percent of the owned company)6

Partly owned company

Sydkraft Birka Energi Graninge Oslo Energi BKK

Owner

company

Sydkraft 20

Graninge 8

Statkraft 177 20 26

When estimating the model using the data from the year 1997, the authors assume that the installed

capacity for all firms is constant and capacity utilization is determined endogenously in the model. The

aim of the simulation is to find how PCO arrangements affected the control variables of the firms in the

industry. Therefore, two cases are compared: the Base Case in which the setting is the PCO web

presented in Table 2 above, and the No Ownership case which represents the scenario where there are

no PCO arrangements. The results for both countries in both cases are presented below:

5 Amundsen & Bergman (2002, p. 83)

6 Amundsen & Bergman (2002, p. 84)

7 Note that there is a cross-border ownership interest between Norwegian Statkraft and Swedish Sydkraft.

Norwegian power producers Swedish power producers

Statkraft 8740 Vattenfall 15350

Oslo Energi 2100 Sydkraft 6000

Hydro Energi 1720 Birka Energi 4570

BKK 1500 STORA Kraft 1320

Lyse Kraft 1480 Skellefteå Kraft 600

Competitive Fringe 12660 Graninge 560

Competitive Fringe 1950

Total 28200 30350


Table 3: Equilibrium Prices (SEK/MWH) and Output (MW) in Sweden in the two cases8

Case Price Total Output Sydkraft Graninge

Base Case 147 19780 4850 550

No Ownership 145 19860 4850 550

Table 4: Prices (SEK/MWH) and Output (MW) in Norway in the two cases9

Case Price Total Output Statkraft

Base Case 147 22270 5200

No Ownership 139 23310 5870

The tables above present the price for electricity in each market, the total industry output, and the

output levels of the biggest firm(s) in that market for the case where PCO schemes are present (Base

Case) and where they are not (No Ownership). It becomes clear that given a certain PCO structure, the

bigger firm, in this case Statkraft since it is the biggest player in both markets, chooses to produce less,

therefore increasing the price. Moreover, the smaller price-taking firms do not change their quantity

choices when compared to the No Ownership case. Accordingly, the profit of Statkraft should increase.

This is shown in the next table:

8 Amundsen & Bergman (2002, p.85)

9 Amundsen & Bergman (2002, p.85)


Table 5: Profit of Statkraft (MSEK/hour) under both ownership assumptions10

Base Case No Ownership

Profit in Statkraft 0.244 0.247

Share of profit in Sydkraft 0.047 -

Share of profit in Oslo Energi 0.016 -

Share of profit in BKK 0.018 -

Total profit 0.325 0.247

From the combined interpretation of the results presented in Tables 3 to 5, it becomes clear, that

with PCO Statkraft reduces its own operating profit (first row of the table above) by choosing a lower

output level. However, due to its shareholding in rivals, it more than offsets the reduction in its own

operating profits.

In conclusion, market power is re-established in this market through the creation of PCO ties

between competitors. According to Amundsen and Bergman (2002, p. 89), it is not necessary for rivals

to merge, anticompetitive concerns arise from PCO already.

10

Amundsen & Bergman (2002, p. 86)


Chapter 5: Competitive AnalysisChapter 5: Competitive AnalysisChapter 5: Competitive AnalysisChapter 5: Competitive Analysis

In the paper by Ezrachi and Gilo (2006) the focus is on the policy aspects of PCO. They discuss the

three different policy instruments in the European Union that can regulate PCO arrangements. The

authors identify two possible effects: unilateral and coordinated.

Unilateral effects are, in the case of PCO, when firms independently behave anti-competitively, for

example by raising their prices above the equilibrium levels. This might cause the rest of the producers

to also raise prices, so that the general price in the market is raised. The authors determine that only

when there is imperfect competition, there is a threat of unilateral effects arising. (Ezrachi & Gilo, 2006,

p. 331)

Coordinated effects take place when an action, such as an investment in a rival, facilitates collusion,

it being tacit or explicit. With PCO firms earn part of their competitors’ profits. Therefore it can be said

that collusion can be more easily sustained, since a deviation given PCO also hurts the deviating firm by

lowering its earnings from PCO. More precisely, by deviating, the firm hurts its competitors’ profits,

which in turn reduce the deviator’s own profits from shareholding. The authors make an important

distinction here: if there is no maverick firm in the industry, i.e. a firm most eager to deviate by

undercutting prices, collusion is not facilitated by PCO arrangements. This is an important point since

under the EC Merger Regulation, a merger involving a maverick firm will call for special attention for

anticompetitive effects.

Malueg (1992) presents the theoretical framework for collusion to be sustained in an infinitely

repeated Cournot duopoly given PCO. For this reason, the next section shows the framework in the case

of price competition.

Collusion

The setting is that of a Bertrand duopoly with symmetric firms. These are assumed to have unit costs

equal to zero. Moreover, the demand function is jii ppq γ+−= 1 and since firms are symmetric it holds

that ];0[21∈v . Firms maximize their profits with respect to prices. From the symmetric case in Chapter

3, the optimal price is:


γ−−

−=

v

vp

Bertrand

22

1

Correspondingly, output and profits are

( )2

2

)22(

)1(1

22

1

γ

γ

γ

γ

−−

−−+=Π

−−

−−=

v

vvv

v

vvq

Bertrand

Bertrand

Next, the collusive profit is determined. Here the firms jointly maximize their profits:

( ) ( ) 01)1(1)1(0:

)1()1(

12122121

1

1122221121

=−+−+−++−+−−⇒=∂

Π∂

+−++−=Π+Π=Π

pppvpvpvpppvp

FOC

qvpqpvqvpqpv

Collusion

Collusion

γγγγ

After drawing symmetry the collusive price is found:

)1(2

1

γ−=Collusion

p

Not surprisingly, it corresponds to the monopoly price under Bertrand competition (v=0). The collusive

output and profits are:

)1(4

1

2

1

γ−=Π

=

Collusion

Collusionq

Finally, the profits of a deviating firm are determined. These correspond to the profit maximization of

the deviating firm, which takes the price and quantities of its rival fixed to be the collusive equilibrium

found above:

( )

0)1(2

121)1(0:

1)1(),(

=

−+−−⇒=

∂

Π∂

++−−=Π

γγ

γ

Deviation

Deviation

Deviation

CollusionCollusionCollusionDeviationDeviationCollusionDeviationDeviation

pvp

FOC

qvppppvpp


Rearranging yields:

)1(4

2

γ

γ

−

−=Deviation

p

Likewise:

( )2

22

)1(16

2

)1(4

2

γ

γγ

γ

γ

−

−−=Π

−

−=

v

q

Deviation

Deviation

The game is a repetition of the static game. There is an infinite number of periods t. Each firm

charges the collusive price, earning collusive profits, if t=0 or if that was the case in the previous period.

Firms turn to the Bertrand competition price as a means of punishment if in the previous period its

competitor charged a price different than the collusive one. Tacit collusion can only be sustained if the

discounted payoffs from colluding exceed the discounted payoffs from deviating. The discount factor is

r+=

1

1δ where r is the interest rate, so that 10 ≤≤ δ . The game is summarised as follows:

( ) ( ) ( )( ) ( ) ( ) ( )22232232

322232

2

2

22

884574892128

613124144524*

)1(16

)1(

11

........

γγγγγγγγγγ

γγγγγγγγ

γ

γδ

δ

δ

δ

δ

δδδδδδ

+−+−−+−−−

+−+−++−++−+−

−

−≥

Π−Π

Π−Π≥

Π+

+Π≥+

Π

Π++Π+Π+Π≥Π++Π+Π+Π

vvv

vvv

BertrandDeviation

CollusionDeviation

BertrandDeviation

Collusion

Bertrand

t

BertrandBertrandDeviationCollusion

t

CollusionCollusionCollusion

Due to the complexity of this expression after substitution it is impossible to draw any conclusions

from it. Also no trend is distinguished from the graphical representation below:


Figure 3. 1: Minimal discount factors that sustain collusion in a Bertrand setting

The graph shows the minimum level of the discount factors (plotted on the vertical axis) for every

value of γ, the coloured series. On the horizontal axis, which values corresponds to the first row of the

table below it, the level of the shares are plotted.

From the table it can be see that except for two values, the one corresponding to (v=0.125; γ=0.5)

and the one corresponding to (v=0.25; γ=0.75), the rest are meaningful. When the discount value is

negative, it means that no matter the value of the discount rate, given 10 ≤≤ δ , collusion can be

sustained. The positive values of δ show that only above that level and up to 1=δ collusion can be

sustained.

Next, the ‘outlier’, i.e. the series belonging to 25.0=γ , in the graph is eliminated so as to have a

clearer view of the remaining series:

0,01 0,125 0,25 0,375 0,5

0,01 0,2472 0,0154 0,0057 0,0026 0,0012

0,25 -533,7162 0,4979 0,1677 0,0714 0,0303

0,5 -4,4515 2,0213 0,4915 0,1764 0,0588

0,75 -2,7528 -8,1266 2,3312 0,4809 0,0857

0,99 -2,9641 -3,4688 -4,2068 -5,4580 0,1101

-550

-450

-350

-250

-150

-50

50

dis

cou

nt

fact

or

δ

v

ga

mm

a


Figure 3. 2: Minimal discount factors that sustain collusion in a Bertrand setting

Again here it is not possible to find a trend. It can only be concluded that for some combinations of

the substitutability parameter and the level of PCO, collusion is clearly facilitated since the minimum

discount rate is below zero. For the cases where it holds that 10 ≤≤ δ , collusion can still be sustained,

but further study is required to clarify whether the values of the discount rate differ from those in the

No Ownership scenario.

The subsequent sections give an insight into the applicability of the European Commission’s policy

instruments to the regulation of PCO arrangements, according to Ezrachi and Gilo (2006).

Regulatory instruments

EC Merger Regulation

This regulatory device, as it name points out, deals mainly with mergers, horizontal or vertical. The

condition ‘for a share acquisition to come within the jurisdiction of the ECMR, it has to fall under the

0,01 0,125 0,25 0,375 0,5

0,01 0,2472 0,0154 0,0057 0,0026 0,0012

0,5 -4,4515 2,0213 0,4915 0,1764 0,0588

0,75 -2,7528 -8,1266 2,3312 0,4809 0,0857

0,99 -2,9641 -3,4688 -4,2068 -5,4580 0,1101

-9

-7

-5

-3

-1

1

3

dis

cou

nt

fact

or

δC

v

ga

mm

a


definition of a Concentration.’ (Ezrachi & Gilo, EC Competition Law and the Regulation of Passive

Investments Among Competitors, 2006, p. 335) By concentration it is meant that a change in control of

the firms concerned has to result from the acquisition of silent shares in rivals. So a PCO arrangement

would only fall under this category if it creates some sort of control, which seems very difficult given

that it is silent or passive interests that are being discussed.

However, according to the authors, even after realizing the anticompetitive concerns that arise from

shareholding, ‘the Commission, backed by the Member States, concluded that the regulation of passive

minority shareholding under the new Merger Regulation should be outside the scope of the merger

regime.’ (Ezrachi & Gilo, 2006, p. 337)

It can be concluded, that PCO arrangements do not fall under the legislation of the EC Merger

Regulation.

Article 81 EC

This article deals with agreements (horizontal or vertical) between firms. It forbids agreements that

harm competition. According to Ezrachi and Gilo (2006) the ECJ holds that an acquisition of shares by

one firm in its competitors does not necessarily mean it distorts competition, however it may cause

other firms in the industry to react to this acquisition by behaving anti-competitively.

Again, Article 81 indicates that competitive concerns arise when the acquisition of equity shares in

rivals results in coordination by firms or realization of control. Therefore, ‘partial equity interests in

oligopolistic settings, which involve some influence of a significant firm in a rival […] or enable the

exchange of competitively sensitive information between competitors, would potentially be subject of

Article 81.’ (Ezrachi & Gilo, 2006, p. 340) Also, an interest acquisition would fall under Article 81 if there

are prospects of a future takeover or if it would raise unilateral anticompetitive concerns.

Article 81 seems to be more appropriate in the regulation of passive investments in rivals than the EC

Merger Regulation, however, its applicability is reduced to a few special scenarios.

Article 82 EC

This last policy instrument forbids the abuse of a dominant position. The authors find that an

acquisition of silent interest would only fall under this article if it would be considered as an abuse of

dominance (Ezrachi & Gilo, 2006, p. 342). Once more, the requirement that a change in control happens


as a consequence of the investment appears in Article 82. Given the low likelihood of one of the firms

abusing a dominant position by acquiring shares in a rival, it can be concluded that the applicability of

this instrument to the case of PCO arrangements is very unlikely.

Summarizing, it can be said that if a PCO investment does not fall under one of the following three

categories,

a) establishment of control

b) facilitation of coordination or existence of some influence between competitors

c) abuse of dominant position

it is not covered by the European Union’s regulation of competition. It becomes clear that it is nearly

impossible for a PCO arrangement to fall under the first or last categories mentioned above. Its

investigation and sanction are only left to the second condition. I think it is clear that the

anticompetitive effects are easily overlooked by the antitrust authorities. Therefore, there is a need for

an expansion of the current Competition Policy to include PCO schemes.


ConclusionConclusionConclusionConclusion

From the modelling of PCO in an industry competing in quantities, it was found that firms choose

lower output levels as a best response to their competitors’ choices in the presence of PCO in the

general case as well as the duopoly and symmetric cases. Firms therefore set higher prices earning

higher profits.

In the case of Bertrand competition, there is a clear influence of PCO shares in the firms’ best

response functions. Unexpectedly in the general case, these have the effect of lowering the price as a

response to the competitors’ choices. When solving the model in the duopoly case, there is once again a

strong relationship between the shares firms own in each other and the price level, but the effect is not

clear.

In Chapter 4, it was shown that when firms engage in PCO arrangements, these affect their output

decisions both in the domestic and in the export markets. Evidence from the Nordic energy market

proves that the consequences of the existence of PCO are that firms maximize their profit functions

taking PCO into account, which leads to lower output levels and increases in prices.

In Chapter 5 it was seen that for many combinations of the substitutability parameter and the level

of PCO shares, the discount factor is negative, suggesting that tacit collusion is easily sustained (for any

level of the discount rate). Nevertheless, no clear pattern was found.

Despite the limitations of the models presented in this thesis, specifically the assumption of

symmetry between firms, it is clear that there is a special need for antitrust authorities to investigate

these practices more thoroughly than they do now. For this purpose, the antitrust regulation in the EU

should be extended to include a more specific and less lenient approach to PCO. Perhaps the best way

to deal with it is to treat it on a case-to-case basis.


AppendixAppendixAppendixAppendix

Cournot Competition

No-ownership Cournot

n asymmetric firms with homogenous goods

i

i

i

ii

ii

i

iii

qP

Pcq

cPqq

P

qFOC

qcP

∂∂

−=⇒

=−+∂

∂⇒=

∂

Π∂

−=Π

00:

)(

General Cournot

)1(

))(1()1(

0)1(0:

)())(1(

∑

∑

∑∑∑

∑∑

∑∑

≠

≠

≠≠≠

≠≠

≠≠

−

−

∂∂

−=⇒

∂

∂−−−−=

∂

∂−

=∂

∂+

−+

∂

∂−⇒=

∂

Π∂

−+−−=Π

n

ij

ji

n

ii

jij

i

i

i

n

ii

j

i

iji

n

ij

ji

i

n

ij

jii

n

ii

j

i

ijii

i

n

ij

ji

i

i

n

ij

jjijii

n

ij

jii

v

qv

qP

Pcq

qq

PvcPv

q

Pvq

qq

PvcPq

q

Pv

qFOC

qcPvqcPv


Duopoly Cournot

( )

( )

( )

( )

( )

2112

21

1

121

2112

1221

2

2

2

1221

12

2

212

1221

2112

1

1

1

1221

2112

212

212

1

1

1

212

212

1

1

2112

211221121221

1

212

212

1

1

2112

2112

1

21

12

121

2

2

12

1

1

1

12

121

2

2

2

21

212

1

1

1

1

1*

1

)1)(1(*

1

1*

1

)1)(1(*

1

)1)(1(

)1(

)1()1)(1(

1

)1()1)(1(1

)1(

)1(

)1(

)1(

vv

v

qP

cPv

vv

vv

qP

Pcq

vv

v

qP

cPv

vv

vv

qP

Pcq

vv

vv

vq

P

cPv

qP

Pcq

vq

P

cPv

qP

Pc

vv

vvvvvvq

vq

P

Pcv

qP

Pc

vv

vvq

v

v

qv

qP

Pcv

qP

Pcq

v

qv

qP

Pcq

v

qv

qP

Pcq

−−

−

∂∂

−+

−−

−−

∂∂

−=⇒

−−

−

∂∂

−+

−−

−−

∂∂

−=⇒

−−

−−

−∂

∂

−+

∂∂

−=

−∂

∂

−+

∂∂

−=

−−

−+−−

−∂

∂

−−

∂∂

−=

−−−

−

−−

∂∂

−

−

∂∂

−=

−−

∂∂

−=

−−

∂∂

−=


Symmetric Case

)1(*

1

1

)1(1

)1(1

)1(1

)1(

vnv

qP

Pcq

qP

Pc

vnv

vnvvnvq

qP

Pc

vn

vnq

vn

vqn

qP

Pcq

+−

∂∂

−=⇒

∂∂

−=

+−

−++−

∂∂

−=

−−

−+

−−

−−

∂∂

−=

Bertrand Competition

No-ownership Bertrand

i

i

i

i

i

i

i

i

i

i

i

i

i

i

iii

i

i

iiii

c

pq

qp

cp

qq

p

qp

p

qcpq

pFOC

qcp

+

∂∂

−=⇒

∂

∂+−=

∂

∂

=∂

∂−+⇒=

∂

Π∂

−=Π

0)(0:

)(


No-ownership Bertrand (specific demand)

0)(

1

=

+−= ∑≠

i

n

ij

jii

qMC

ppq γ

2

)1(2

1

)1(2

1

)1(2

12

)1(2

)1(1)1(2

)1(2

1)1(

)1(2

11

)1(2

1

1))1(2(

0)1(21

:

0210:

)1(

−−=Π⇒

−−=⇒

−−

−+−+−=

−−

−+−−−=

−−−+

−−−=

−−=⇒

−=−+−

=−+−

=

=+−⇒=∂

Π∂

+−==Π

∑

∑

≠

≠

n

nq

n

nn

n

nn

nn

nq

np

np

pnp

ppsymmetry

ppp

FOC

pppqp

i

i

i

i

i

ii

ji

n

ij

ji

i

i

n

ij

jiiiii

γ

γ

γ

γγγγ

γ

γγ

γγ

γ

γ

γ

γ

γ

γ

General Bertrand

i

i

n

ij

ji

n

ij

jji

jij

i

i

i

i

i

n

ij

jj

i

j

iji

n

ij

jiii

i

in

ij

ji

n

ij

jj

i

j

ijii

i

i

i

n

ij

ji

i

i

n

ij

jjjijiii

n

ij

jii

pq

v

cpp

qv

c

pq

qp

cpp

qvqvcp

p

qv

cpp

qvcp

p

qqv

pFOC

qcpvqcpv

∂∂

−

−∂

∂

−+

∂∂

−=⇒

−∂

∂−−−=−

∂

∂−

=−∂

∂+

−

∂

∂+−⇒=

∂

Π∂

−+−−=Π

∑

∑

∑∑∑

∑∑

∑∑

≠

≠

≠≠≠

≠≠

≠≠

)1(

)(

)()1()()1(

0)()()1(0:

)())(1(


Bertrand duopoly

))(1()1)(1(4

)1()1)(1(2

))(1()1)(1(4

)1)(1()1)(1(2

))(1()1)(1(4

)1)(1(4

)1(4

)1()1(2

)1(4

)1()1(2

)1)(1(4

))(1()1)(1(4

)1(4

)1()1(2

)1)(1(4

)1)(1(1

)1(4

)1(

2

1

)1(2

)1(

)1(2

)1(1

)1(2

)1(

2

1

)1(2

)1(

2

1

)1(2

)1(

2

1

)1(22

1

)1(2

)1(

2

1

)1(22

1

)1(1

)1(

1

0

1

2

1221

2

2112

2

122112212112

1

2

1221

2

2112

1221122112

1

2

1221

2

2112

2112

21

122121

1

21

122121

2112

2

1221

2

2112

1

21

122121

2112

21121221

2

1

21

1221

12

2112

21

1221

1

12

2112

1

21

1221

1

12

2112

1

12

1211

2

21

1221

2

21

2122

1

21

212

211

1

121

21

212

1

1

21

1

vvvv

vvvvvvp

vvvv

vvvvvp

vvvv

vv

v

vvvp

v

vvv

vv

vvvvp

v

vvv

vv

vvvvp

v

vv

v

vv

v

vvp

v

vvp

v

vvp

v

vvp

v

pvpp

v

vvp

v

pvpp

v

pvppp

pq

v

pp

qv

pq

ppp

c

ppq

i

jii

−−−−−

−+−+−−=⇒

−−−−−

+−−+−−=

−−−−−

−−

−

+−+−=

−

+−+−=

−−

−−−−−

−

+−+−=

−−

+−+−−

−

+−+=

−

+−

−

+−−

−

+−+

−

+−+=

−

+−+=

−+

+=⇒

−

+−+=

−+

+=⇒

−++−=

∂∂

−

∂∂

−

∂∂

+−−=

=

+−=

γ

γ

γ

γ

γ

γ

γγ

γγ

γγγ

γγ

γγγ

γγγ

γγ

γ

γ


( )( )

( )( )( )

[ ]( )

( )( )

( ) ( )( )

( ) ( )( )

( )( )

( )))(1()1)(1(4

1)1)(1(2

))(1()1)(1(4)1(

1)1()1()1(2

))(1()1)(1(4)1(

1)1()1)(1()1)(1(2

))(1()1)(1(4)1(2

2122214

))(1()1)(1(4)1(2

)1()1(2)1(

))(1()1)(1(4)1(2

)21()1(4)1(

))(1()1)(1(4)1(2

)1()1)(1(2)1(

))(1()1)(1(4)1(2

))(1()1)(1(4)1(

))(1()1)(1(4

)1()1)(1(2

)1(2

)1(

2

1

2

1221

2

2112

2

212112122112

2

2

1221

2

211212

2

212112121221

2

12

2

2

1221

2

211212

2

21211212122112122112

2

2

1221

2

211212

2

2112

2

2121

2

12

2

1221121221

2

12

2

1221122112

2

2

1221

2

211212

2

12211221211221122112

2

1221

2

211212

2

122112

2

21

2

2112122112

2

2

1221

2

211212

2

1221122121122112

2

1221

2

211212

2

1221

2

211212

2

2

1221

2

2112

2

122112212112

12

2112

2

vvvv

vvvvvvp

vvvvv

vvvvvvvp

vvvvv

vvvvvvvvvvp

vvvvv

vvvvvvvvvvvvvvvvp

vvvvv

vvvvvvvvvv

vvvvv

vvvvvvvvvp

vvvvv

vvvvvvvv

vvvvv

vvvvvp

vvvv

vvvvvv

v

vvp

−−−−−

−+−+−−=⇒

−−−−−−

−+−−+−−=

−−−−−−

−+−−+−−−−−=

−−−−−−

+−−++−+−++−−=

−−−−−−

−+−++−−+−+

−−−−−−

−+−−+−−−=

−−−−−−

−+−+−−+−+

−−−−−−

−−−−−−=

−−−−−

−+−+−−

−

+−+=

γ

γ

γ

γ

γ

γ

γ

γ

γ

γγ

γ

γ

γ

γγ

γ

γ

γ

γγ


Symmetric Bertrand

ppp

ccc

vvv

ji

ji

jiij

==

==

==

in

ij

ji

n

ij

jjij

ji

i

i

i

i

n

ij

ji

n

ij

jji

jij

i

i

ii

c

v

cpvpp

p

c

pq

v

cpp

qv

pq

qp

+

−−

−

−−

+−−=

+

∂∂

−

−∂

∂

−

∂∂

−=

∑

∑

∑

∑

≠

≠

≠

≠

)1)(1(

)(

1

1

)1(

)(

γγ

Establishing symmetry:

( ) ( )

( ) ( )

( )( )

( )( ) γ

γ

γ

γ

γγγγγγ

γγγ

γγγ

γγ

−−−

−−−−+−−=⇒

−−−

−−

−−

−−−−+−−=

−−

−−−−+−−=

−−

+−−+−−−

−−

−−−−+=

−−

−−−−−−−

−−

−−+=

−−

−−−+

+−−

−−++−=

vn

vnvncvnp

vn

vn

vn

vnvncvnp

vn

vnvncvn

vn

vnvvnvvnp

vn

vnvnc

vn

vnvnvnp

vn

vnc

vn

vnp

cvn

cpvnppp

)1(12

)1()1(1)1(1

)1(12

)1(1

)1(1

)1()1(1)1(1

)1(1

)1()1(1)1(1

)1(1

)1(12

)1(1

)1()1(11

)1(1

)1()1(1)1(12

)1(1

)1(11

)1(1

)1(11

)1(1

)()1(1


Application

( )

( )

( )

( )

∑

∑

∑

∑∑

∑

∑

∑

∑∑

∑∑

∑∑

∑

∑

≠

≠

≠

≠≠

≠

≠

≠

≠≠

≠≠

≠≠

≠

≠

−

−

∂∂

+−=⇒

∂

∂−

∂

∂−−−−−

=

−

−

∂∂

−=⇒

∂

∂−

∂

∂−−−−

=

=

∂

∂+

−−+

∂

∂−⇒=

∂

∂

=

∂

∂+

−+

∂

∂−⇒=

∂

∂

−+−++

−+−+−=ΠΠ

N

ij

ij

j

N

ij

ji

i

R

RCRi

i

N

ij i

Rij

j

i

RN

ij

jiRCiR

N

ij

ij

i

N

ij

ij

j

N

ij

ji

i

C

Ci

i

N

ij i

C

ij

j

i

CN

ij

jiiC

N

ij

ij

i

j

i

RN

ij

jiRCiRi

i

RN

ij

ij

i

i

j

i

CN

ij

jiiCi

i

CN

ij

ij

i

i

jRCjjjjRjC

N

ij

ji

iRCiiiiRiC

N

ij

ijjii

CC

CC

RC

CC

CC

RC

C

RC

CC RC

CC

RC

RCCC

CCC

CC

CC

RC

CC

CC

CC

CC

CC

CC

C

CC

CC CC

CC

CC

CCCC

CCC

CC

CC

CC

RC

RCCC

CCCRC

RCCC

CC

RC

C

CC

CCCC

CCCCC

CCCC

CC

CC

C

RCRCCCCRCCC

CC

CC

RCRCCCCRCCC

CC

CCCCC

v

qv

qP

PCq

q

Pv

qq

PvCPv

q

v

qv

qP

PCq

q

Pv

qq

PvCPv

q

qq

PvCPq

q

Pv

q

VFOC

qq

PvCPq

q

Pv

q

VFOC

qqqCqPqPv

qqqCqPqPvV

)1(

)1(

)1(

)1(

)1(

)1(

0)1(0:

0)1(0:

)(

)()1(),(

;

;

;

;

;

;

;

;

;

;

;

;

;

;

;

;

;

;;

;

;

;

;;

;;;;;

;;;;;

;

;

;2

1

;

;

ϕ

ϕ

ϕ

ϕ

ϕ


BibliographyBibliographyBibliographyBibliography

Alley, W. A. (1997). Partial Ownership Arrangements and Collusion in the Automobile Industry. The

Journal of Industrial Economics Vol. 45, No. 2 , 191-205. Online [Retrieved May 25, 2009, from JSTORL

http://www.jstor.org]

Amundsen, E. S., & Bergman, L. (2002). Will Cross-Ownership Re-Establish Market Power in the Nordic

Power Market. The Energy Journal Vol.23 No. 2 , 73-95. Online [Retrived May 25, 2009, from ProQuest:

http://proquest.umi.com]

Church, J., & Ware, R. (2000). Industrial Organization: A strategic approach. United States of America:

Irwin, McGraw-Hill. Online [Retrieved May 25, 2009, from University of Calgary:

http://homepages.ucalgary.ca]

Dietzenbacher, E., Smid, B., & Volkerink, B. (2000). Horizontal integration in the Dutch financial sector.

Interational Journal of Industrial Organization Vol. 18 , 1223-1242. Online [Retrived May 25, 2009, from

Science Direct: http://www.sciencedirect.com]

Ezrachi, A., & Gilo, D. (2006). EC Competition Law and the Regulation of Passive Investments Among

Competitors. Oxford Journal of Legal Studies Vol. 26 No. 2 , 327-349. Online [Retrived May 25, 2009,

from Oxford Journals: http://ojls.oxfordjournals.org]

Flath, D. (1991). When is it rational for firms to acquire silent interests in rivals? International Journal of

Industrial Organization Vol. 9 , 573-583. Online [Retrived May 25, 2009, from Science Direct:

http://www.sciencedirect.com]

Gilo, D., Mosche, Y., & Spiegel, Y. (2006). Partial cross ownership and tacit collusion. The Rand Journal of

Economics Vol. 37 No. 1 , 81-99. Online [Retrived May 25, 2009, from ProQuest:

http://proquest.umi.com/]

Malueg, D. A. (1992). Collusive behavior and partial ownership of rivals. International Journal of

Industrial Organization Vol. 10 , 27-34. Online [Retrived May 25, 2009, from Science DIrect:

http://www.sciencedirect.com]

Motta, M. (2004). Competition Policy, Theory and Practice. Cambridge: Cambridge University Press.

Purohit, D., & Staelin, R. (1994). Rentals, sales, and buybacks: Managing secondary distribution channels.

Journal of Marketing Research Vol. 31 No. 3 , 325-338. Online [Retrived May 25, 2009, from ProQuest:

http://proquest.umi.com]

Reynolds, R. J., & Snapp, B. R. (1986, June). The Competitive Effects of Partial Equity Interests and Joint

Ventures. International Journal of Industrial Organization 4 , 141-153. Online [Retrived May 25, 2009,

from Science Direct: http://www.sciencedirect.com]


US Antitrust Division. (n.d.). Clayton Act, Section 7. Online [Retrieved May 02, 2009, from Antitrust

Division Manual Chapter II: http://www.usdoj.gov]

von der Fehr, N.-H., Fabra, N., & Harbord, D. (2002). Modeling Electricity Auctions. The Electricity

Journal , 72-79. Online [Retrieved April 20, 2009, from EconWPA:

http://129.3.20.41/eps/game/papers/0206/0206001.pdf]

Documents

The effects of Partial Cross-Ownership on competition