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Introduction Model Exercise Incentive to Collude Antitrust Policy
CollusionCabral Chapter 9
Yuta Toyama
Last updated: October 27, 2019
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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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
Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
Derivation (if time allows)
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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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Introduction Model Exercise Incentive to Collude Antitrust Policy
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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