Price-Fixing and Repeated Games

Price-Fixing and Repeated Games
Chapter 10: Price-fixing and Repeated Games

Chapter 10: Price-fixing and Repeated Games
Collusion and cartels What is a cartel? attempt to enforce market discipline and reduce competition between a group of suppliers cartel members agree to coordinate their actions prices market shares exclusive territories prevent excessive competition between the cartel members Chapter 10: Price-fixing and Repeated Games

Collusion and cartels 2 Cartels have always been with us; generally hidden electrical conspiracy of the 1950s garbage disposal in New York Archer, Daniels, Midland the vitamin conspiracy But some are explicit and difficult to prevent OPEC De Beers shipping conferences Chapter 10: Price-fixing and Repeated Games

Recent events Recent years have seen record-breaking fines being imposed on firms found guilty of being in cartels. For example illegal conspiracies to fix prices and/or market shares €479 million imposed on Thyssen for elevator conspiracy in 2007 €396.5 million imposed on Siemens for switchgear cartel in 2007 $300 million on Samsung for DRAM cartel in 2005 Hoffman-LaRoche $500 million in 1999 UCAR $110 million in 1998 Archer-Daniels-Midland $100 million in 1996 Chapter 10: Price-fixing and Repeated Games

Recent cartel violations 2
Justice Department Cartel Fines grew steadily since 2002 Chapter 10: Price-fixing and Repeated Games

Cartels Two implications cartels happen generally illegal and yet firms deliberately break the law Why? pursuit of profits But how can cartels be sustained? cannot be enforced by legal means so must resist the temptation to cheat on the cartel Chapter 10: Price-fixing and Repeated Games

The incentive to collude
Is there a real incentive to belong to a cartel? Is cheating so endemic that cartels fail? If so, why worry about cartels? Simple reason without cartel laws legally enforceable contracts could be written De Beers is tacitly supported by the South African government gives force to the threats that support this cartel not to supply any company that deviates from the cartel Investigate incentive to form cartels incentive to cheat ability to detect cartels Chapter 10: Price-fixing and Repeated Games

An example Take a simple example two identical Cournot firms making identical products for each firm MC = $30 market demand is P = Q Q = q1 + q2 Price 150 Demand 30 MC 150 Quantity Chapter 10: Price-fixing and Repeated Games

The incentive to collude
Profit for firm 1 is: p1 = q1(P - c) = q1(150 - q1 - q2 - 30) = q1(120 - q1 - q2) Solve this for q1 To maximize, differentiate with respect to q1: p1/q1 = 120 - 2q1 - q2 = 0 q*1 = 60 - q2/2 This is the best response function for firm 1 The best response function for firm 2 is then: q*2 = 60 - q1/2 Chapter 10: Price-fixing and Repeated Games

The incentive to collude 2
Nash equilibrium quantities are q*1 = q*2 = 40 Equilibrium price is P* = $70 Profit to each firm is (70 – 30)x40 = $1,600. Suppose that the firms cooperate to act as a monopoly joint output of 60 shared equally at 30 units each price of $90 profit to each firm is $1,800 But there is an incentive to cheat firm 1’s output of 30 is not a best response to firm 2’s output of 30 Chapter 10: Price-fixing and Repeated Games

The incentive to cheat Suppose that firm 2 is expected to produce 30 units Then firm 1 will produce qd1 = 60 – q2/2 = 45 units total output is 75 units price is $75 profit to firm 1 is $2,025 and to firm 2 is $1,350 Of course firm 2 can make the same calculations! We can summarize this in the pay-off matrix: Chapter 10: Price-fixing and Repeated Games

The Incentive to cheat 2 Both firms have the incentive to cheat on their agreement This is the Nash equilibrium Firm 2 Cooperate (M) Deviate (D) Cooperate (M) (1800, 1800) (1250, 2025) Firm 1 (1600, 1600) Deviate (D) (2025, 1250) (1600, 1600) Chapter 10: Price-fixing and Repeated Games

The incentive to cheat 3 This is a prisoners’ dilemma game mutual interest in cooperating but cooperation is unsustainable However, cartels to form So there must be more to the story consider a dynamic context firms compete over time potential to punish “bad” behavior and reward “good” this is a repeated game framework Chapter 10: Price-fixing and Repeated Games

Finitely repeated games
Suppose that interactions between the firms are repeated a finite number of times know to each firm in advance opens potential for a reward/punishment strategy “If you cooperate this period I will cooperate next period” “If you deviate then I shall deviate.” once again use the Nash equilibrium concept Why might the game be finite? non-renewable resource proprietary knowledge protected by a finite patent finitely-lived management team Chapter 10: Price-fixing and Repeated Games

Finitely repeated games 2
Original game but repeated twice Consider the strategy for firm 1 first play: cooperate second play: cooperate if firm 2 cooperated in the first play, otherwise choose deviate Firm 2 Firm 1 Cooperate (M) Deviate (D) (1800, 1800) (1250, 2025) (2025, 1250) (1600, 1600) Chapter 10: Price-fixing and Repeated Games

This strategy is unsustainable the promise is not credible at end of period 1 firm 2 has a promise of cooperation from firm 1 in period 2 but period 2 is the last period dominant strategy for firm 1 in period 2 is to deviate Firm 2 Firm 1 Cooperate (M) Deviate (D) (1800, 1800) (1250, 2250) (2250, 1250) (1600, 1600) Chapter 10: Price-fixing and Repeated Games

Promise to cooperate in the second period is not credible but suppose that there are more than two periods with finite repetition for T periods the same problem arises in period T any promise to cooperate is worthless so deviate in period T but then period T – 1 is effectively the “last” period so deviate in T and so on Selten’s Theorem “If a game with a unique equilibrium is played finitely many times its solution is that equilibrium played each and every time. Finitely repeated play of a unique Nash equilibrium is the equilibrium of the repeated game.” Chapter 10: Price-fixing and Repeated Games

Selten’s theorem applies under two conditions The one-period equilibrium for the game is unique The game is repeated a finite number of times Relaxing either of these two constraints leads to the possibility of a more cooperative equilibrium as an alternative to simple repetition of the one-shot equilibrium Here, we focus on relaxing the second constraint and consider how matters change when the game is played over an infinite or indefinite horizon Chapter 10: Price-fixing and Repeated Games

Repeated games with an infinite horizon
With finite games the cartel breaks down in the “last” period assumes that we know when the game ends what if we do not? some probability in each period that the game will continue indefinite end period then the cartel might be able to continue indefinitely in each period there is a likelihood that there will be a next period so good behavior can be rewarded credibly and bad behavior can be punished credibly Chapter 10: Price-fixing and Repeated Games

Valuing indefinite profit streams
Suppose that in each period net profit is pt Discount factor is R Probability of continuation into the next period is r Then the present value of profit is: PV(pt) = p0 + Rrp1 + R2r2p2 +…+ Rtrtpt + … valued at “probability adjusted discount factor” Rr product of discount factor and probability of continuation Chapter 10: Price-fixing and Repeated Games

Trigger strategies Consider an indefinitely continued game potentially infinite time horizon Strategy to ensure compliance based on a trigger strategy cooperate in the current period so long as all have cooperated in every previous period deviate if there has ever been a deviation Take our earlier example period 1: produce cooperative output of 30 period t: produce 30 so long as history of every previous period has been (30, 30); otherwise produce 40 in this and every subsequent period Punishment triggered by deviation Chapter 10: Price-fixing and Repeated Games

Cartel stability Expected profit from sticking to the agreement is: PVM = Rr R2r2 + … = 1800/(1 - Rr) Expected profit from deviating from the agreement is PVD = Rr R2r2 + … = Rr/(1 - Rr) Sticking to the agreement is better if PVM > PVD this requires 1800/(1 - Rr) > Rr/(1 - Rr) or Rr > (2.025 – 1.8)/(2.025 – 1.6) = 0.529 if r = 1 this requires that the interest rate is less than 89% if r = 0.6 this requires that the interest rate is less than 14.4% Chapter 10: Price-fixing and Repeated Games

value of R < 1 for which
Cartel stability 2 There is always a value of R < 1 for which this equation is satisfied This is an example of a more general result Suppose that in each period profits to a firm from a collusive agreement are pC profits from deviating from the agreement are pD profits in the Nash equilibrium are pN we expect that pD > pC > pN Cheating on the cartel does not pay so long as: This is the short-run gain from cheating on the cartel This is the long-run loss from cheating on the cartel pD - pC Rr > pD - pN The cartel is stable if short-term gains from cheating are low relative to long-run losses if cartel members value future profits (low discount rate) Chapter 10: Price-fixing and Repeated Games

Trigger Strategy Issues
With infinitely repeated games cooperation is sustainable through self-interest But there are some caveats examples assume speedy reaction to deviation what if there is a delay in punishment? trigger strategies will still work but the discount factor will have to be higher harsh and unforgiving particularly relevant if demand is uncertain decline in sales might be a result of a “bad draw” rather than cheating on agreed quotas so need agreed bounds on variation within which there is no retaliation or agree that punishment lasts for a finite period of time Chapter 10: Price-fixing and Repeated Games

The Folk theorem Have assumed that cooperation is on the monopoly outcome this need not be the case there are many potential agreements that can be made and sustained – the Folk Theorem Suppose that an infinitely repeated game has a set of pay-offs that exceed the one-shot Nash equilibrium pay-offs for each and every firm. Then any set of feasible pay-offs that are preferred by all firms to the Nash equilibrium pay-offs can be supported as subgame perfect equilibria for the repeated game for some discount factor sufficiently close to unity. Chapter 10: Price-fixing and Repeated Games

$1800 to each firm may not be sustainable but something less will be
The Folk theorem 2 Take example 1. The feasible pay-offs describe the following possibilities p2 The Folk Theorem states that any point in this triangle is a potential equilibrium for the repeated game $1800 to each firm may not be sustainable but something less will be $3600 Collusion on monopoly gives each firm $1800 $2000 If the firms collude perfectly they share $3,600 If the firms compete they each earn $1600 $1800 $1600 p1 $1500 $1600 $1800 $2000 $3600 Chapter 10: Price-fixing and Repeated Games

Balancing temptation A collusive agreement must balance the temptation to cheat In some cases the monopoly outcome may not be sustainable too strong a temptation to cheat But the folk theorem indicates that collusion is still feasible there will be a collusive agreement: that is better than competition that is not subject to the temptation to cheat Chapter 10: Price-fixing and Repeated Games

Empirical Application: Estimating the Effects of Price Fixing
An important question for policy-makers and scholars alike is precisely what is the effect of cartels when they do happen. Basically, how different is the market price set by a cartel from the price that would have prevailed in the absence of the cartel? Both theory and empirical technique can be used to determine this “but for” price, the price that would have prevailed “but for” the cartel. Chapter 10: Price-fixing and Repeated Games

담합효과에 대한 경제분석 담합의 존부 공정위 심의에서 합의의 증거가 명확하지 않은 상황에서 담합의 존재 혹은 부재를 입증하는 보조적 증거로 담합의 가격인상효과 검증 예) 산업용 화약 담합( )에서 담합 중단의 효과로 가격인하가 실제 있었는지 계량경제학적으로 검증 담합의 손해액 담합 손해배상의 민사소송에서 담합으로 인한 가격인상(price overcharge)과 손해액의 추정 예) 군납유류 입찰담합( )에서 담합 손해액 추정에서 중회귀분석을 활용한 이중차분법(DID) 적용

담합으로 인한 가격인상분(overcharge)의 산정방법
유형 산정방법 비담합 가격 “before-and-after” 전후 비교법 담합 전과 후의 가격 비교 담합 전 가격 “yardstick” 표준시장 비교법 담합이 없는 유사 상품 시장과의 비교 다른 상품시장 가격 “dummy” 더미변수 모형 담합/비담합 기간(혹은 시장)의 가격과 수요, 공급 요인 및 담합더미 변수 사이의 관계를 통계적으로 추정 담합 더미변수의 영향을 제거한 가격 “forecasting” 예측 모형 비담합 기간(혹은 시장)의 가격과 수요, 공급 요인 변수 사이의 관계를 통계적으로 추정 추정된 관계식에 담합기간(시장)의 설명변수를 대입하여 예측한 가격 “cost-based” (“margin”) 비용기반 모형 과거의 마진 자료에 기초한 경쟁 가격 추정 costs plus margin 과점 이론 모형의 응용 과점 경쟁의 이론 모형을 구성 모형의 추정치에 기초한 이론적 경쟁가격

Dummy v. Forecasting Model
더미나 예측 모형은 전후 혹은 표준시장 비교법의 아이디어에 담합 이외의 다른 변수의 효과를 함께 고려하는 계량경제학의 중회귀분석(multiple regression, 종속변수의 변화를 여러 독립변수의 변화로 구분하여 설명하려는 시도)으로 일반화한 것 더미나 예측 모형이 시계열자료(time-series, 담합/비담합 기간)에 적용되면 전후 비교법을 일반화한 것이 되고, 횡단면자료(cross-section, 담합/비담합 시장)에 적용되면 표준시장 비교법의 아이디어를 일반화한 것 더미모형은 담합 이외에 가격에 영향을 주는 다양한 요인들(예컨대 수요 및 비용 요인들)을 통제한 후에 담합더미(담합시기 혹은 담합시장에 1의 값, 비담합시기 혹은 비담합시장에 0의 값 부여)의 효과로 담합효과를 추정  담합/비담합 기간(시장) 자료를 모두 활용하는 장점 예측모형은 담합시기(시장)의 각 기간(시장)에 각기 다른 더미를 채택하는 것과 사실상 마찬가지  기간(시장)별로 담합효과가 달라질 수 있는 신축성을 허용하는 장점

DID: Difference-in-Difference, 이중차분법
담합/비담합 시기(time series)와 담합/비담합 시장(cross section)이 함께 존재하는 경우(panel)에는 전후 비교법과 표준시장 비교법을 함께 고려하여 담합의 효과를 보다 정확하게 추정할 수 있음 담합시장 (군납유류) 비담합시장 (한전, 항공사 등 민간) 차분 담합시기 (1998,1999,2000) 110 80 30 담합시기의 담합시장과 비담합시장의 차이 비담합시기 (1995,1996,1997, 2001,2002,2003) 90 75 15 비담합시기의 20 담합시장의 담합시기와 비담합시기의 차이 5 비담합시장의 이중차분

중회귀분석을 이중차분법 패널(시계열+횡단면)자료가 존재하는 경우 담합시기의 더미와 담합시장의 더미 그리고 수요 및 비용 요인 등의 그 밖의 가격결정 요인들을 설명변수로 하여 가격을 변화를 설명하는 모형 P: 가격 유류 입찰가격 X: 담합 이외의 가격을 설명하는 제반 설명 변수 환율, 원유도입가, 납품조건, 수송수단, 외환위기 등 DCM: 담합시장더미(Dummy of Collusive Market) 담합시장인 군납유류의 경우는 1, 그 외의 경우는 0 DCT: 담합시기더미(Dummy of Collusive Time) 담합시기인 1998, 1999, 2000년의 시기는 1, 그 외의 경우는 0 위의 식에서 의 추정값이 바로 이중차분에 의한 담합효과를 나타냄

군납유류 입찰담합(2000) 사례 공정위 의결 ( ) – 1998~2000년 3년간 군납유류 입찰 담합에 대해 1,901억원 과징금 및 고발 조치 손해배상 민사소송 제1심 판결( ) – 이중차분법에 의한 감정분석에 의거 손해배상액을 810억원으로 결정 항소심 판결( ) – 싱가포르 국제 현물시장 가격기준인 MOPS(Means of Platt’s Singapore)를 표준가격(yardstick)으로 하여 손해배상액을 1,309억원으로 산정 대법원 판결( ) – “담합기간 동안 국내 군납유류 시장은 과점체제 하의 시장이어서 완전경쟁시장에 가까운 싱가포르 현물시장과 동일한 시장으로 볼 수 없다”며 손해배상액을 다시 산정하라고 항소심판결을 파기 환송 파기환송 재판부의 권유에 따라서 제1심의 손해액배상액으로 양측이 화해

군납유류 입찰담합(2000) 사례 손해배상액 추정을 둘러싼 원고, 피고, 감정인 사이의 논란
원고 (국방부) – 싱가포르 MOPS 가격을 기준으로 1584억원 주장 피고 (5개 정유사) – 2003년 KDI에 의뢰한 용역연구 결과 이중차분법에 따라서 302억원의 손해배상액 추정. 항소심에서는 2008년 연대세 교수진의 이중차분법의 수정 분석 결과로 188억원 제시 감정인( 서울대 기업경쟁력센터) 년 이분차분법에 의한 원감정 분석결과로 1,140억원의 손해액 추정. 서강대 교수진의 비판을 일부 수용한 보완감정 분석에서는 1,120원으로 손해액 조정 대법원 판결의 의의 담합 손해배상 사건에 있어서, 시지남용 사건에서의 포스코 판결에 준하는, 판정의 기본 원칙 제시

군납유류 입찰담합(2000) 사례 대법원 판결의 의의
“가상적 경쟁가격은 담합행위가 발생한 당해 시장의 다른 가격형성 요인을 그대로 유지한 상태에서 담합행위로 인한 가격상승분만을 제외한 방식으로 산정해야 한다.” 이는 사실상 경제학의 중회귀분석 방법론의 기본 취지와 완전히 부합 즉 중회귀분석에 의한 담합 손해액 산정방법은 담합 이외에도 다양한 요인들이 가격에 영향을 미치는 상황에서 관련된 제반의 상품, 시장 및 경제 조건의 변화 효과를 적절히 통제한 후에 담합에 따른 가격인상분만을 분리해 내는 것

Summary Infinite/indefinite repetition raises possibility of price-fixing stable cartels sustained by credible threats so long as discount rate is not too high and probability of continuation is not too low Public Policy concern about cartels is justified Deterrence is at least as important as breaking up existing cartels Deterrence rises with probability of detection and punishment if caught Cartels happen as evidenced by numerous recent cases and price effects can be large, say as much as 33 percent Chapter 10: Price-fixing and Repeated Games

Introduction Collusion is difficult to detect no detailed information on costs can only infer behavior Where is collusion most likely? look at the cartel member’s central problem cooperation is necessary to sustain the cartel but on what should the firms cooperate? take an example duopolists with different costs Chapter 10: Price-fixing and Repeated Games

Market Features that Aid Collusion
Potential for monopoly profit demand relatively inelastic ability to restrict entry common marketing agency persuade consumers of advantages of buying from agency members low search costs security trade association control access to the market persuade consumers that buying from non-members is risky use marketing power Chapter 10: Price-fixing and Repeated Games

Features Aiding Collusion 2
Low costs of reaching a cooperative agreement small number of firms in the market lowers search, negotiation and monitoring costs makes trigger strategies easier and speedier to implement similar production costs avoids problems of side payments detailed negotiation misrepresentation of true costs lack of significant product differentiation again simplifies negotiation – don’t need to agree prices, quotas for every part of the product spectrum Chapter 10: Price-fixing and Repeated Games

Low cost of maintaining the agreement use mechanisms to lower cost of detecting cheating basing-point pricing use mechanisms to lower cost of detecting cheating most-favored customer clauses guarantees rebates if new customers are offered lower prices meet-the-competition clauses guarantee to meet any lower price removes temptation to cheat look at a simple example Chapter 10: Price-fixing and Repeated Games

Meet-the-competition clause
 the one-shot Nash equilibrium is (Low, Low)  meet-the-competition clause removes the off-diagonal entries  now (High, High) is easier to sustain Firm 2 High Price Low Price High Price 12, 12 5, 14 5, 14 Firm 1 Low Price 14, 5 14, 5 6, 6 Chapter 10: Price-fixing and Repeated Games

Frequent market interaction makes trigger strategy more effective Stable market conditions makes detection of cheating easier with uncertainty need a modified trigger strategy punish only for a set period of time punish only if sales/prices fall outside an agreed range Chapter 10: Price-fixing and Repeated Games

An Example: Collusion on NASDAQ
NASDAQ is a very large market Traders typically quote two prices “ask” price at which they will sell stock “bid” price at which they will buy stock at the time of the analysis prices quoted in eighths of a dollar prices determined by the “inside spread” lowest ask minus highest bid price profit on the “spread” difference between the ask and the bid price competition should result in a narrow spread but analysis seemed to indicate wider spreads inside spreads had high proportion of “even eighths” Chapter 10: Price-fixing and Repeated Games

Collusion on NASDAQ 2 Suggestion that this was evidence of collusion NASDAQ dealers engaged in a repeated game past and current quotes are public information to dealers so dealers have an incentive to cooperate on wider spreads Look at an example Chapter 10: Price-fixing and Repeated Games

Antitrust Policy & Collusion
Ideally, antitrust policy can act to deter cartel formation To do this, authorities must investigate/monitor industries and, when wrongdoing is found, prosecute and punish However, the authorities can not monitor every market. So, for any cartel, there is only a probability that it will be investigated and discovered Assume: Probability of investigation is a; Probability of successful prosecution given investigation is s Punishment if successfully prosecuted if fine, F Chapter 10: Price-fixing and Repeated Games

Antitrust Policy & Collusion 2
Combining our investigation and prosecution assumptions with our earlier model of collusion yields the following expected profit for each cartel member as M – asF + 1 –  VC = 1 – (1 – as) In our earlier analysis a = s = F = 0. It is clear in examining the above equation that an increase in either the probability of investigation a, or in the probability of successful prosecution s, or in the punishment | fine F, will decrease expected cartel profits and so make cartel formation less likely MORAL: Policy against cartels works by deterring their formation in the first place and not perhaps so much as by breaking them up once they happen Chapter 10: Price-fixing and Repeated Games

Antitrust Policy & Collusion 3
Which tool the authorities should rely most on— a, s, or F—depends on a number of factors. Even a small fine may do the trick if the probability of detection and prosecution as is high enough. However, monitoring, investigating, and prosecuting are expensive whereas fines are relatively costless to impose. This suggests that optimal policy will cut back on expensive detection efforts and balance this by imposing heavy fines for those cartels that are detected. Chapter 10: Price-fixing and Repeated Games

Cartel Detection Cartel detection is far from simple most have been discovered by “finking” even with NASDAQ telephone tapping was necessary If members of a cartel are sophisticated they can hide the cartel: make it appear competitive Chapter 10: Price-fixing and Repeated Games

Birmingham Steel Company
Basing Point Pricing Pittsburgh Then it was priced at the mill price plus transport costs from Pittsburgh Suppose that the steel is made here And that it is sold here Birmingham Steel Company Chapter 10: Price-fixing and Repeated Games

Antitrust Policy: Leniency/Amnesty
Play the cartel members against each other by offering amnesty or leniency to the firm that provides evidence to indict the others However, the possibility of avoiding penalties increases the ex-ante value of joining a cartel May lead to the formation of more cartels even as more a caught and prosecuted Chapter 10: Price-fixing and Repeated Games

■ 감면제도의 이해 Prisoners’ Dilemma (용의자의 고민)
기업 B 자신신고 미신고 기업 A 자진신고 -250, -250 0, -1000, 0 -50, 공동행위로 적발시 기업 A, B는 각각 1000억의 과징금 납부 두 기업 모두 자진 신고시, 1순위일 확률을 0.5로 가정하면 기대과징금은 각각 0.5* *500 = 250억 한 기업만 자신신고시 기대과징금은 신고기업 0, 미신고 기업 1000억 두 기업 모두 미신고시, 공정위의 자체조사로 적발될 확률을 0.05로 가정하면 기대과징금은 각각 0.05*1000 = 50억

Evidence on Leniency Only real world data is on cartels that were caught, which is not a random sample Hinloopen and Soetevent (2006) test leniency programs in a laboratory experiment They found that leniency Made cartel formation more difficult Made defection more likely Made defecting firms defect more All of which worked to lower prices Chapter 10: Price-fixing and Repeated Games

Price-Fixing and Repeated Games

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Price-Fixing and Repeated Games

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