Econ 445, Spring 2014 Industrial Organization
advertisement
Econ 545, Spring 2016 Industrial Organization Anticompetitive actions: Cartels and collusion Collusion and cartels Goals • We consider what circumstances and events allow cartels to remain together. • We consider what policy actions are possible to prevent cartels from forming or break them apart if they do form. • We will consider how cartels stay together when their illegality prevents explicit contracts. Broader importance • Cartels hurt consumers with artificially high prices. • US and EU antitrust authorities actively pursue and prosecute collusive behavior. Econ 445: Anticompetitive actions 2 Collusion and cartels What is a cartel? • Cooperation among firms to increase their profit relative to noncooperative equilibrium. • How is this implemented? Agreements to set: - Prices - Market shares or quantities - Exclusive territories to serve • These agreements sacrifice welfare to increase profits. Prices and DWL increase Econ 445: Anticompetitive actions 3 Collusion and cartels Cartels are illegal in U.S. but still occur. Examples: • Garbage disposal in New York prosecuted in mid-1990s • Bid-ask margins on NASDAQ in 1980s and early 1990s • ADM in lysine (animal feed additive) in mid-1990s • Samsung in DRAM (computer memory) in early 2000s Cartels can operate in the open abroad: • OPEC for oil • De Beers for diamonds US and EU governments search for and prosecute cartels. Total values of fines have grown, with many billion dollars in fines assessed in last 10 years. Econ 445: Anticompetitive actions 4 Collusion and cartels Implications of illegality: • Because collusion is illegal, groups of firms cannot write contracts to enforce pricing arrangements. • There are incentives to cheat on cartel agreements. - Charge a low price when all others are charging high. • To last, cartels members must believe it is in their own self interest to continue collusive behavior. Two types of collusive arrangement: • Tacit: Unspoken agreement for coordinated action. • Explicit: With communication among firms in cartel. Perhaps more precise, but generates evidence. Econ 445: Anticompetitive actions 5 Gains from collusion, example A market with demand of π = 150 − π has: • Two identical firms (A and B) with πΆ ππ = 30ππ . • If competing, the firms choose ππ΄ and ππ΅ simultaneously. When firms are not cooperating: • Firms have response functions ππ = 60 − 0.5π−π • Equilibrium ππ ’s are 40, so π = 80 and π = 70. • Each firm has profit of $1,600. When firms are cooperating: • Monopoly (total) output is ππ = 60 and ππ = 90. • Could have each firm produce ππ = 30. • If firms share profit evenly, each gets $1,800. Econ 445: Anticompetitive actions 6 Gains from collusion, example At the cooperative outcome, firms are not best-responding to each other. • They still have ππ = 60 − 0.5π−π . • If ππ΅ = 30, then A’s best response is ππ΄ = 45. • When A cheats and B cooperates, π = 75 and π = 75. • Profit when A “defects” on collusive agreement: ππππππ‘π΄ = 75 − 30 × 45 = $2,025 ππππππ‘π΅ = 75 − 30 × 30 = $1,350 • Comparison of profit: Cheating>Monopoly>Non-cooperative>Cheated-upon Econ 445: Anticompetitive actions 7 Gains from collusion, example In a payoff matrix, the payoffs from playing the cooperative or noncooperative strategies are: Firm B Cooperate Don’t Cooperate Cooperate 1800 , 1800 1350 , 2025 Don’t Cooperate 2025 , 1350 1600 , 1600 Firm A • The simultaneous-move equilibrium is that each firm chooses the non-cooperative action. • Very similar to the Prisoner’s Dilemma Econ 445: Anticompetitive Actions 8 Repeated interaction • The one-shot game avoids the cartel outcome. Self-interested firms cannot resist the non-cooperative profit. • Cartels of (own-)profit maximizing firms do happen. How? • Firms compete over time in a repeated game. • This allows a change to reward cooperation and punish defection. • We saw a repeated game in the chain-store paradox example, which did not allow a long-term strategy different from one-shot equilibrium. Will this be different? Econ 445: Anticompetitive actions 9 Finite interaction • Suppose firms A and B compete with each other for a known and finite number of time periods (T). • The number of periods could be determined by: - A production license held by A and B that expires. - Management teams with finite contracts or careers. • We will ask whether the following reward/punishment strategy is possible in equilibrium: - I will begin the game by cooperating. - If you cooperate too, I will cooperate again next period. - If you fail to cooperate, I will not cooperate next period and (possibly) never cooperate again. Econ 445: Anticompetitive actions 10 Finite interaction with T=2 Assume that game lasts for two periods with each period’s actions and payoffs in the previous payoff matrix. Firm B Cooperate Don’t Cooperate Cooperate 1800 , 1800 1350 , 2025 Don’t Cooperate 2025 , 1350 1600 , 1600 Firm A • In period 2 both firms should expect non-cooperative behavior. There is no opportunity to punish afterwards. • In period 1, the threat of future punishment is empty because A and B anticipate what will happen next. Econ 445: Anticompetitive Actions 11 Finite and infinite interaction • If T=2, the firms take non-cooperative actions in both periods. • What happens if the game is repeated three times (T=3)? • In general, when T is finite and known, backward induction implies that cooperation is not a subgame perfect equilibrium. • What if the firms do not know when the game will end? - Can think of this as a repeated game of infinite length. - Could be because there is always a chance for “tomorrow”. • When there is a great enough chance for later choices: - “Good” behavior has an opportunity to be rewarded. - “Bad” behavior has an opportunity to be punished. Econ 445: Anticompetitive actions 12 Valuing indefinite profit streams • Suppose that in each period net profit is ππ‘ • Discount factor is R (= 1/(1+r)) • Probability of the game continuing to the next period is π. - As of today, the probability of tomorrow existing is π. - As of today, the probability of the day after tomorrow happening is π2 • The present value of a stream of profits is: - ππ·π = π0 + π ππ1 + π 2 π2 π2 + π 3 π3 π3 + β― - π π is a probability-adjusted discount factor. The future is far away, plus it might not even happen Econ 445: Anticompetitive actions 13 Trigger strategies • In a trigger strategy, my current choice is triggered or determined by my competitors’ previous choices. • We will work with the “grim trigger” strategy: - Cooperate now if no other firm has defected in a previous period. Note this covers first period. - Defect forever (play non-cooperative strategy) if any other firm has ever defected in the past. • Similar but less harsh: Tit for tat. - Cooperate in first period. - In all subsequent periods, do whatever competitor did in previous period. Econ 445: Anticompetitive actions 14 Cartel stability Back to the example of firms A and B considering cooperating (K) at the monopoly output, so cartel profit is as large as possible. • Each firm’s present value from choosing cooperation (K) now and forever while the other also cooperates: 1800 πΎ 2 2 ππ·π = 1800 + π π × 1800 + π π × 1800 + β― = 1 − π π • Each firm’s present value from defecting now and taking the punishment outcome forever, beginning next period: 1600π π π· 2 2 ππ·π = 2025 + π π × 1600 + π π × 1600 + β― = 2025 + 1 − π π • It is better to remain in the cartel when ππ·π πΎ > ππ·π π· . When does this happen? 1800 1600π π > 2025 + 1−π π 1−π π 2025 − 1800 π π > = 0.529 2025 − 1600 Econ 445: Anticompetitive actions 15 Cartel stability What does π π > 0.529 mean? • If we are sure tomorrow will happen (π = 1), then π > 0.529 1 - Using π = , this happens if π < 89% 1+π - Interpret this as the effective interest rate for the time between moves. If a period is one year, this is huge. • If tomorrow happens only with 60% probability (π = 0.6), then: - Need π > .8817 - Equivalent to π < 13.4%, still a high interest rate. • In all, if players think that the future will happen (π not small) and value what happens there (R not small) cooperation can happen (i.e., a cartel can be stable. Econ 445: Anticompetitive actions 16 Cartel stability Now take a more general look at the stability condition. ππ·π πΎ > ππ·π π· ππΎ (1−π π) > ππ· + π π > π π > π πππΆ (1−π π) ππ· −ππΎ ππ· −ππΆ ππ· −ππΎ ππ· −ππΎ + ππΎ −ππΆ Benefit from cheating Benefits from cheating and stability • Cartel stability is good for firms when the discount value (π π) is large relative to the proportional short-term benefit of cheating. Econ 445: Anticompetitive actions 17 Cartel stability: twists Now we consider a few features that affect cartel stability. Timing and supervision: • If we fix a discount rate of R or Rπ per period, but allow firms to monitor each others’ behavior only every other period … - Cheating becomes more beneficial (it takes longer to get caught), and R must be larger to sustain collusion. • If interaction or monitoring happens more frequently, this reduces the benefits of cheating, which makes cartels more stable. Econ 445: Anticompetitive actions 18 Cartel stability: twists What can affect cartel stability? • Number of firms Illustrative example: Return to our Cournot example … - Two symmetric firms: π π· = 2025, π πΎ = 1800, π πΆ = 1600 π π· − π πΎ 2025 − 1800 π π > π· = = 0.529 πΆ π −π 2025 − 1600 π· - Three symmetric firms: π = 1600, π πΎ = 1200, π πΆ = 900 π π· − π πΎ 1600 − 1200 π π > π· = = 0.571 πΆ π −π 1600 − 900 With N=3, a smaller range of discount values allow collusion. Econ 445: Anticompetitive actions 19 Cartel stability: twists What can affect cartel stability? • Differences between firms • Any successful agreement must make the cartel’s hardest-to-please member happy to participate. • Product and cost differences lead to challenges or complexity in … - How to set prices or market shares to generate total and individual profit. - How to monitor many distinct prices or shares across cartel members. - Deciding who is hurt by cheating and who should punish Econ 445: Anticompetitive actions 20 Cartel possibilities • Suppose that Rπ is not large enough to support collusion where cartel members receive full monopoly profits. • In our Cournot duopoly example, this is Rπ < 0.529. Is a cartel impossible? • No. The “folk theorem” says that for any Rπ it is possible to identify some sustainable cartel that is better than π πΆ . Folk Theorem: Any distribution of profits that are preferred by all firms to the NE profits of the one-period game can be supported as a subgame perfect equilibrium for an infinite repeated game for some discount factor sufficient close to unity. • The key is to adjust π π· and π πΎ so that cheating is no longer beneficial. Example: If the duopoly cartel sets ππ = 36, π πΎ = 1728 but π π· = 1764. This allows Rπ as low as 0.220. Econ 445: Anticompetitive actions 21 Cartel possibilities • The folk theorem result signals that we can expand our ideas about what a cartel can do. • Another important possibility: Relaxing the grim trigger. • Suppose that demand fluctuates randomly. - You are a member of a cartel producing ππ = 30. - The mean expected price is 90, but what if you see P=75? - Did your partner just cheat, or was there a demand shock? • The grim trigger demands punishing forever, even if no one cheated. • A better arrangement is to define a trigger price (e.g. 82) and if price ever falls beneath it, begin a brief punishment. Econ 445: Anticompetitive actions 22 Public Policy In the US, the DOJ’s and FTC’s responsibilities include policing markets for signs of cartel activity. Why is this hard? • Firms act to minimize evidence. Tacit collusion has no paper trail at all. • Firms will not admit that prices are high due to collusion – many alternative explanations can be offered. • Investigations are not always successful. Policy instruments: • Enforcement effort: Let s be the change of getting caught. • Penalty size: Let $F be the penalty from getting caught. Econ 445: Anticompetitive actions 23 Public Policy How do s and F affect the payoff from collusion? • Suppose a cartel has existed until today, and a member weighs defecting vs. continuing in the cartel. Assume π = 1. • If a firm defects, it is acting non-cooperatively and not in danger of prosecution. Write ππ·π π· as π π· , ππ·π πΎ as π πΎ . Payoff is (still): πΆπ π ππ· = ππ· + 1−π • If the firm remains in the cartel, its π πΎ combines two parts: π πΎ = Pr πππ’πβπ‘ × ππππ’π πππ’πβπ‘ + Pr ~πππ’πβπ‘ × ππππ’π ~πππ’πβπ‘ ππΎ • ππππ’π πππ’πβπ‘ = −πΉ+ • ππππ’π ~πππ’πβπ‘ =π πΎ + Rπ πΎ ππΆ π 1−π Combine these to learn π πΎ Econ 445: Anticompetitive actions 24 Public Policy Value from being in a cartel: πΆ π π πΎ πΎ π =π π −πΉ+ + 1 − π π πΎ + π π πΎ 1−π Simplify to isolate π πΎ : πΆ π π π πΎ π − π πΉ + 1−π ππΎ = 1− 1−π π This is lower than our previous ππ·π πΎ = π πΎ /(1 − π ). Antitrust enforcement reduces the benefits from being in a cartel. • Defection is now more attractive. • Firms less likely to join cartels, cartels more likely to fail. • Can reduce π πΎ through s or F. Can be cheaper for the gov’t to raise F rather s, which takes more effort. Econ 445: Anticompetitive actions 25 Public Policy: amnesty • Antitrust authorities use amnesty or leniency programs. • How this works: If a cartel firm preemptively confesses to being in a cartel, it gets little or no punishment (πΉ ≈ 0). • Intended effect: Additional incentive to defect from cartel. • Unintended effect: Joining cartels can be more attractive. - With a leniency program, joining a cartel can be less costly because now there is a zero-punishments way out. - Possible plan: I will join a cartel, take π πΎ for a while, and then bail out (through defection or amnesty) before I’m cheated upon or go to jail. • US and EU leniency programs have been successful in generating confessions, but absolute success is uncertain. Econ 445: Anticompetitive actions 26 Conclusions What we covered: • The challenges of cooperation when doing so is illegal • Discounting future payoffs from infinite interaction • Firm’s decisions to remain in a cartel vs. break apart. • Market factors that make cartels easier or harder to maintain. • Public policy can make cartels harder to create and sustain What is coming next: • Legal cooperation between firms. • Vertical relations between firms. Econ 445: Anticompetitive actions 27
