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

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Collusion and cartels 2 Recent events • Recent years have seen record-breaking fines being • Cartels have always been with us; generally hidden imposed on firms found guilty of being in cartels. For – electrical conspiracy of the 1950s example – garbage disposal in New York – illegal conspiracies to fix prices and/or market shares – Archer, Daniels, Midland – €479 million imposed on Thyssen for elevator conspiracy in 2007 – the vitamin conspiracy – €396.5 million imposed on Siemens for switchgear cartel in 2007 • But some are explicit and difficult to prevent – $300 million on Samsung for DRAM cartel in 2005 –OPEC – Hoffman-LaRoche $500 million in 1999 – De Beers – UCAR $110 million in 1998 – shipping conferences – Archer-Daniels-Midland $100 million in 1996

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Recent cartel violations 2 Cartels

• Justice Department Cartel Fines grew steadily since 2002 • 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

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1 The incentive to collude An example • Is there a real incentive to belong to a cartel? • Is cheating so endemic that cartels fail? • Take a simple example • If so, why worry about cartels? – two identical Cournot firms making identical products – for each firm MC = $30 • Simple reason – market demand is P = 150 - Q – without cartel laws legally enforceable contracts could be written –Q = q + q De Beers is tacitly supported by the South African government 1 2 Price • gives force to the threats that support this cartel 150 – not to supply any company that deviates from the cartel • Investigate Demand – incentive to form cartels – incentive to cheat – ability to detect cartels 30 MC

150 Quantity

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The incentive to collude The incentive to collude 2

Profit for firm 1 is:  = q (P - c) • quantities are q*1 = q*2 = 40 1 1 • Equilibrium price is P* = $70 = q (150 - q -q - 30) 1 1 2 • Profit to each firm is (70 – 30)x40 = $1,600. = q1(120 - q1 -q2) • Suppose that the firms cooperate to act as a monopoly – joint output of 60 shared equally at 30 units each To maximize, differentiate with respect to q1: – price of $90 1/q1 = 120 - 2q1 -q2 = 0 – profit to each firm is $1,800 q* = 60 - q /2 •But 1 2 – there is an incentive to cheat The function for firm 2 is then: • firm 1’s output of 30 is not a best response to firm 2’s output of 30

q*2 = 60 - q1/2

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The incentive to cheat The Incentive to cheat 2 • Suppose that firm 2 is expected to produce 30 units d • Then firm 1 will produce q 1 = 60 – q2/2 = 45 units – total output is 75 units – price is $75 Firm 2 – profit to firm 1 is $2,025 and to firm 2 is $1,350 Cooperate (M) Deviate (D) • Of course firm 2 can make the same calculations!

• We can summarize this in the pay-off matrix: Cooperate (M) (1800, 1800) (1350, 2025) Firm 1 Deviate (D) (2025, 1350) (1600,(1600, 1600)1600)

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2 The incentive to cheat 3 Finitely repeated games • This is a prisoners’ dilemma game • Suppose that interactions between the firms are repeated a – mutual interest in cooperating finite number of times known to each firm in advance – but cooperation is unsustainable – opens potential for a reward/punishment • However, cartels to form •“If you cooperate this period I will cooperate next period” • So there must be more to the story • “If you deviate then I shall deviate.” – once again use the Nash equilibrium concept – consider a dynamic context • firms compete over time • Why might the game be finite? • potential to punish “bad” behavior and reward “good” – non-renewable resource –this is a repeated game framework – proprietary knowledge protected by a finite patent – finitely-lived management team

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Finitely repeated games 2 Finitely repeated games 3 • Original game but repeated twice • This strategy is unsustainable • Consider the strategy for firm 1 – the promise is not credible – first play: cooperate • at end of period 1 firm 2 has a promise of cooperation from – second play: cooperate if firm 2 cooperated in the first play, firm 1 in period 2 otherwise choose deviate • but period 2 is the last period • dominant strategy for firm 1 in period 2 is to deviate

Firm 2 Firm 2

Cooperate (M) Deviate (D) Cooperate (M) Deviate (D)

Cooperate (1800, 1800) (1350, 2025) Cooperate (1800, 1800) (1350, 2025) (M) (M) Firm 1 Firm 1 Firm Deviate (D) (2025, 1350) (1600, 1600) Deviate (D) (2025, 1350) (1600, 1600)

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Finitely repeated games 4 Finitely repeated games 5 • Promise to cooperate in the second period is not credible • Selten’s theorem applies under two conditions – but suppose that there are more than two periods – The one-period equilibrium for the game is unique • with finite repetition for T periods the same problem arises – in period T any promise to cooperate is worthless – The game is repeated a finite number of times – so deviate in period T • Relaxing either of these two constraints leads to the – but then period T – 1 is effectively the “last” period possibility of a more cooperative equilibrium as an – so deviate in T . . . and so on alternative to simple repetition of the one-shot equilibrium • Selten’s Theorem – “If a game with a unique equilibrium is played finitely many times • Here, we focus on relaxing the second constraint and its solution is that equilibrium played each and every time. Finitely consider how matters change when the game is played repeated play of a unique Nash equilibrium is the equilibrium of the repeated game.” over an infinite or indefinite horizon

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3 Repeated games with an infinite horizon Valuing indefinite profit streams

• With finite games the cartel breaks down in the “last” period • Suppose that in each period net profit is t – assumes that we know when the game ends • Discount factor is R – what if we do not? • some probability in each period that the game will • Probability of continuation into the next period is p continue • Define “probability adjusted discount factor” Rp • indefinite end period • Then the present value of profit is: • then the cartel might be able to continue indefinitely 2  t t – in each period there is a likelihood that there will be a next –PV(t) =  Rp R p  +…+ R p t + …  t period –PV(t) =     +…+  t + … – so good behavior can be rewarded credibly – product of discount factor and probability of continuation – and bad behavior can be punished credibly

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Trigger strategies Cartel stability • Consider an indefinitely continued game • Expected profit from sticking to the agreement is: – potentially infinite time horizon – PVM = 1800 + 1800 + 1800 + … = 1800/(1 - ) • Strategy to ensure compliance based on a • Expected profit from deviating from the agreement is – cooperate in the current period so long as all have cooperated in every previous period – PVD = 2025 + 1600 + 1600 + … = 2025 + 1600/(1 - ) – deviate if there has ever been a deviation • Sticking to the agreement is better if PVM > PVD • Take our earlier example – this requires 1800/(1 - ) > 2025 + 1600/(1 - ) – period 1: produce cooperative output of 30 –or  = Rp (2025 – 1800)/(2025 – 1600) = 0.529 – period t: produce 30 so long as history of every previous period has been (30, 30); otherwise produce 40 in this and every subsequent – Note that R=1/(1+r) period •if p = 1 this requires that the interest rate (r) is less than 89% • Punishment triggered by deviation •if p = 0.6 this requires that the interest rate (r) is less than 13.4%

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Cartel stability 2 Trigger Strategy Issues • With infinitely repeated games • This is an example of a more general result – cooperation is sustainable through self-interest • Suppose that in each period • But there are some caveats C – profits to a firm from a collusive agreement are  – examples assume speedy reaction to deviation D – profits from deviating from the agreement are  • what if there is a delay in punishment? N – profits in the Nash equilibrium are  – trigger strategies will still work but the discount factor will – we expect that D > C > N have to be higher • Cheating on the cartel does not pay so long as: – harsh and unforgiving D - C • particularly relevant if demand is uncertain Rp> D - N – decline in sales might be a result of a “bad draw” rather than cheating on agreed quotas • The cartel is stable – so need agreed bounds on variation within which there is no – if short-term gains from cheating are low relative to long-run losses retaliation – or agree that punishment lasts for a finite period of time – if cartel members value future profits (high discount rate or low interest rate )

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4 The Folk theorem The Folk theorem 2 • Have assumed that cooperation is on the monopoly • Take example 1. The feasible pay-offs describe the following possibilities  – this need not be the case The Folk Theorem states – there are many potential agreements that can be made and that any point in this $3600 sustained – the Folk Theorem triangle is a potential $2000 equilibrium for the Suppose that an infinitely repeated game has a set of pay-offs repeated game that exceed the one-shot Nash equilibrium pay-offs for each and every firm. Then any set of feasible pay-offs that are preferred $1800 by all firms to the Nash equilibrium pay-offs can be supported as perfect equilibria for the repeated game for some $1600 discount factor sufficiently close to unity.

 $1500 $1600 $1800 $2000 $3600

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Balancing temptation Antitrust Policy & Collusion • A collusive agreement must balance the temptation to cheat • Ideally, antitrust policy can act to deter cartel formation • In some cases the monopoly outcome may not be • To do this, authorities must investigate/monitor industries sustainable and, when wrongdoing is found, prosecute and punish – too strong a temptation to cheat – However, the authorities can not monitor every market. – So, for any cartel, there is only a probability that it will be • But the folk theorem indicates that collusion is still feasible investigated and discovered – there will be a collusive agreement: – Assume: Probability of investigation is a; • that is better than competition Probability of successful prosecution given • that is not subject to the temptation to cheat investigation is s Punishment if successfully prosecuted and fine is F

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Antitrust Policy & Collusion 2 Antitrust Policy & Collusion 3 • Combining our investigation and prosecution assumptions with our • Which tool the authorities should rely most on— a, s, or F— earlier model of collusion yields the following expected profit for each depends on a number of factors. cartel member as M –asF + N • Even a small fine may do the trick if the probability of 1 –  VC = detection and prosecution as is high enough. 1 – (1 – as) • In our earlier analysis a = s = F = 0. It is clear in examining the above • However, monitoring, investigating, and prosecuting are equation that an increase in either the probability of investigation a, or expensive whereas fines are relatively costless to impose. This in the probability of successful prosecution s, or in the punishment | suggests that optimal policy will cut back on expensive fine F, will decrease expected cartel profits and so make cartel detection efforts and balance this by imposing heavy fines for formation less likely those cartels that are detected. • 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

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5 Empirical Application: Estimating the Empirical Application: Estimating the Effects of Price Fixing Effects of Price Fixing 2

• An important question for policy-makers and scholars alike is • Kwoka (1997) provides an interesting econometric study that precisely what is the effect of cartels when they do happen. yields information on the “but for” price in the case of a real Basically, how different is the market price set by a cartel from estate cartel in the Washington, D.C. area the price that would have prevailed in the absence of the cartel? • Because of foreclosure as well as for other reasons, real estate • Both theory and empirical technique can be used to determine properties are often sold at auctions. In the DC area during the this “but for” price, the price that would have prevailed “but 1980’s, realtors established a bidding cartel that agreed to for” the cartel. submit artificially low prices with one cartel member chosen to win the auction the price at a low bid P.

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Empirical Application: Estimating the Empirical Application: Estimating the Effects of Price Fixing 3 Effects of Price Fixing 4 • If the true market value of the real estate is V, the winner of the knockout round gets V – K. In equilibrium, the losers and • After the public auction, the cartel members would meet and winners will only be satisfied with their respective outcomes if S hold a private “Knockout” auction. Denote the winning bid in = V – K. So, we can write: this round as K. K – P NK + (N – 1)P – NP N(K – P) V = K + S = K + = P + • Suppose that there were N cartel members. After compensation N - 1 = N –1 N –1 of the original buyer, each of the N – 1 losers in the knockout • Kwoka then assumes that cartel members set the public round would then receive a payment of S = (K – P)/(N –1). winning bid P in constant proportion to the true value V such that V = mP . Substitution and solving for K then yields: (N –1) K = P + (m –1) P N

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Empirical Application: Estimating the Summary Effects of Price Fixing 5 • Infinite/indefinite repetition raises possibility of price-fixing • Kwoka (1997) knows K, P, and N. He uses ordinary regression – stable cartels sustained by credible threats analysis to estimate the slope term m – 1 and hence, m. Using • so long as discount rate is not too high different assumptions about the auction and the compensation of • and probability of continuation is not too low knockout round losers. He estimates m is between 1.48 and 1.88. • Public Policy concern about cartels is justified • Recall that P = V/m. These estimates then imply that the bid- – Deterrence is at least as important as breaking up existing cartels rigging cartels led to public bids that were somewhere between – Deterrence rises with 54% and 67% of the true value. • probability of detection and • punishment if caught • In other words, the bid-rigging cartel depressed public auction prices by somewhere on the order of 33% to 46%. • Cartels happen as evidenced by numerous recent cases and price effects can be large, say as much as 33 percent

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