cabral chapter 9 yuta toyama last updated: october 27, 2019 · i similar argument is applied to...

Introduction Model Exercise Incentive to Collude Antitrust Policy

CollusionCabral Chapter 9

Yuta Toyama

Last updated: October 27, 2019

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Introduction

I Collusion: firms make secret cooperation with each other in order toraise price and earn more profits.

I Cartel: association of suppliers to maintain prices at a high level andrestrict competition among them.

I Good for firms, but for consumers and total welfare. Prohibited incompetition laws.

I We have so many examples of cartels and collusion.I Collusion among companies in public procurement (so called “Dango” in

Japan).I Oil cartel by OPEC (Organization of Petroleum Exporting Countries).I Lysine price-fixing (the animal feed additive):

I “The Informant!” https://www.youtube.com/watch?v=3SooBX1-kIQ

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Case: Vitamin CartelsI Brief history:

I 1989: Start collusion between Roche and BASF. Later invite others (RP,Japanese makers, etc)

I 1999: RP applied for Corporate Leniency Program (end of cartels).

QUESTIONS Why did some cartels survive for a decade while

others collapsed after only a few years?

How does the incentive to collude change with: (1) demand, (2) fringe supply, & (3) merger?

8

25

50

75

100

125

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

(Jan

uary

199

5 =

100)

Beta Carotene

Vitamin A

Vitamin E

Vitamin C

I See Igami and Sugaya (2018, Working Paper) for the details.3 / 19


Goal of this lecture

I We study

1. How firms can cooperate with each other to maintain high price?

2. What affects firms’ incentive to collude?

3. What is the role of public policy (government regulation)?

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Collusion in a static game

I Consider Bertrand game with 2 firms.I Market demand Q(P)I Constant marginal cost c , same for both firms.

I Nash equilibrium: (p1, p2) = (c , c)

I Suppose that firm 1 and 2 meet and make an agreement:I Charge p1 = p2 = p∗, where p∗ is the price charged by “monopolist”.I Split the market demand by half.

I Do firms have an incentive to follow this agreement?

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p1 = p2 = p∗ is not NE!

I Given that p2 = p∗,firm 1 has an incentive to undercut the price:p1 = p∗ − ε, so that firm 1 can get all the demand!

I Same situation as Prisoner’s dilemma:I Firms can obtain higher payoff if cooperate.I But, cooperation is not the best response!

I Under what situation can firms cooperate? =⇒ long-term relationship

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Repeated GameI Consider the repeated game

I Two firms play the following game in every period forever.

I

Firm 2High Low

Firm 1High (10,10) (0,15)Low (15,0) (5,5)

I Possible strategy 1: Firms play (Low, Low) in every period.I This is NE (and SPNE). Given that other firm play “Low”, no incentive to

deviate.

I Possible strategy 2: Trigger strategyI In the period 1 (t = 1), a firm plays “High” in the first period.I After the period 2 (t ≥ 2), a firm plays “High” as long as both players

have kept play (High, High). If not, a firm plays “Low”.

I Trigger strategy can be a subgame perfect Nash equilibrium if both firmsare sufficiently patient.

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I Suppose that your opponent plays trigger strategy.

I Compare the payoff if (1) you follow trigger strategy, and the payoff if(2) you deviate

\period 1 2 · · · t t + 1 t + 2 · · ·Trigger 10 10 10 10 10 · · ·

Deviation 10 10 15 5 5 · · ·

I Discounted sum of the future payoffsI Trigger: 10 + δ10 + δ210 + · · · = 10/(1− δ)I Deviation: 15 + δ5 + δ25 + · · · = 15 + 5δ/(1− δ)

I Trigger strategy is the subgame perfect Nash equilibrium if

10

1− δ> 15 +

5δ

1− δ⇐⇒ δ > 0.5

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General Case

I Consider the repeated game : Both firms have discount factor δ

Firm 2C D

Firm 1C (πC , πC ) (πL, πD)D (πD , πL) (πN , πN)

I Trigger strategy is a NE if

πC1− δ

> πD +δ

1− δπN

⇐⇒ δ >πD − πCπD − πN

I Collusion would be easier (i.e., the above condition is more likely tohold) ifI Deviation payoff πD is lower.I Cooperation payoff πC is higher.I πN is lower.

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Exercise: Repeated Bertrand Game

I Two firms play a Bertrand game in infinitely many periods.

I Marginal cost: c

I Demand Q(P) = 100− P.

I Let pm be the monopoly price.I Consider trigger strategy:

I Play pm at t = 1I Play pm as long as firms have been playing (pm, pm) in the previous

periods. If not, play p = c

I Find the range of discount factor δ in which trigger strategy is thesubgame perfect Nash equilibrium.

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I Step 1: Calculate profit under cooperation (p1 = p2 = pm)

I Step 2: Calculate profit when p1 = p2 = c .

I Step 3: Calculate profit when a firm deviates (given that the opponentplays trigger strategy).

I Step 4: Compare profits.

I (on white board)

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Exercise: Repeated Cournot Game

I Two firms play a Cournot game in infinitely many periods.

I Same setup.

I Denote the quantity produced by monopolist as qm

I Denote the quantity produces in a static (one-shot) Cournot game qc .I Consider trigger strategy:

I Play qm/2 at t = 1I Play qm/2 as long as firms have been playing (qm/2, qm/2) in the

previous periods. If not, play qc

I Find the range of discount factor δ in which trigger strategy is thesubgame perfect Nash equilibrium.

I You can solve in a similar step as in repeated Bertrand game.

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Derivation (if time allows)

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Comparison between Cournot and Bertrand

I Bertrand: Trigger strategy is a SPNE if

δ > 1/2

I Cournot: Trigger strategy is a SPNE if

δ >576

1088≈ 52.9%

I Intuition: Static Nash outcome in Bertrand (p1 = p2 = c) is harsh,making them incentives to collude.

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What affects incentives to collude?

1. InformationI We have assumed that firms can perfectly observe what the opponents do.I For example, if there is a time lag to get information, this increases the

return from deviation, making collusion difficult.

2. The number of firms (in the next slide)

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Market Structure: The number of firms.

I Consider the repeated Bertrand game.

I Now, consider N firms in the market.I Higher N makes collusion more difficult

I Payoff from trigger strategy: 11−δ

πm

N

I Payoff from deviation: πm + δ1−δ0

I Intuition: More firms leads to lower payoff from collusion.

I Similar argument is applied to Cournot model.

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Antitrust Policies

I Collusion is illegal in antitrust laws.I Collusion leads to loss of consumer surplus.I Thus, firms tend to secretly collude.

I Collusion is often observed in public procurement.

I Leniency program:I The firm who first provide information about a cartel is waived of fine (or

receives the reduction of fine).I This provides firms in a cartel an incentive to break the cartel.I More on this in the next slide

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Source: https://www.jftc.go.jp/files/about leniency.pdf

1

A total of 5 violators including before and after JFTC’s investigation are permitted to file an application for surcharge reduction or immunity.

(Up to 3 applicants after the investigation start date.)

A

Jap

an

Fair T

rad

e C

om

mis

sio

n

(Befo

re th

e in

vesti-

gatio

n s

tart d

ate

)(O

n o

r Afte

r the

investig

atio

n s

tart d

ate

)

A’

C

D

E

B

Order of

application

(% of reduction)

1) (100%)

2) (50%)

3) (30%)

4) (30%)

5) (30%)

Joint application

Company

group

Expansion of the Number of Leniency Applicants

Joint Application

Upon certain conditions being met, two or more violators within the same company group will be permitted to jointly file an application for surcharge reduction or immunity.

All the applicants will bw assigned the same order of application.

About the Leniency Program

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cabral chapter 9 yuta toyama last updated: october 27, 2019 · i similar argument is applied to...

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