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Chapter 7 Collusion and Cartels

Chapter 7 Collusion and Cartels. 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

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Chapter 7 Collusion and Cartels

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  1. Chapter 7Collusion and Cartels Industrial Organization: Chapter 7

  2. 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 Industrial Organization: Chapter 7

  3. Collusion and Cartels • Cartels have always been with us • electrical conspiracy of the 1950s • garbage disposal in New York • Archer, Daniels, Midland • the vitamin conspiracy • Some are explicit and difficult to prevent • OPEC • De Beers • shipping conferences Industrial Organization: Chapter 7

  4. Collusion and Cartels • Other less explicit attempts to control competition • formation of producer associations • publication of price sheets • peer pressure (NASDAQ?) • violence • Cartel laws make cartels illegal in the US and Europe • Authorities continually search for cartels • Have been successful in recent years • Nearly $1 billion in fines in 1999 Industrial Organization: Chapter 7

  5. Collusion and Cartels • What constrains cartel formation? • they are generally illegal • per se violation of anti-trust law in US • substantial penalties if prosecuted • cannot be enforced by legally binding contracts • the cartel has to be covert • enforced by non-legally binding threats or self-interest • cartels tend to be unstable • there is an incentive to cheat on the cartel agreement • MC > MR for each member • cartel members have the incentive to increase output • OPEC until very recently Industrial Organization: Chapter 7

  6. 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 by cartel members • 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 • Without contracts the temptation to cheat can be strong Industrial Organization: Chapter 7

  7. The Incentive to Cheat • Take a simple example • two identical Cournot firms making identical products • for each firm MC = $30 • market demand is P = 150 – Q where Q is in thousands • Q = q1 + q2 Price 150 Demand 30 MC Quantity 150 Industrial Organization: Chapter 7

  8. The Incentive to Cheat 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 Industrial Organization: Chapter 7

  9. The Incentive to Cheat These best response functions are easily illustrated q2 q*1 = 60 - q2/2 q*2 = 60 - q1/2 120 Solving these gives the Cournot-Nash outputs: R1 qC1 = qC2 = 40 (thousand) 60 The market price is: C 40 PC = 150 - 80 = $70 R2 Profit to each firm is: q1 p1= p2=(70 - 30)x40 = $1.6 million 40 60 120 Industrial Organization: Chapter 7

  10. The Incentive to Cheat (cont.) What if the two firms agree to collude? They will agree on the monopoly output q2 This gives a total output of 60 thousand 120 Each firm produces 30 thousand Price is PM = (150 - 60) = $90 R1 Profit for each firm is: 60 p1= p2=(90 - 30)x30 = $1.8 million C 40 30 R2 q1 30 40 60 120 Industrial Organization: Chapter 7

  11. The Incentive to Cheat (cont.) Both firms have an incentive to cheat on their agreement If firm 1 believes that firm 2 will produce 30 units then firm 1 should produce more than 30 units q2 Cheating pays!! 120 Firm 1’s best response is: qD1 = 60 - qM2/2 = 45 thousand R1 Total output is 45 + 25 = 70 thousand Price is PD = 150 - 75 = $75 60 C Profit of firm 1 is (75 - 30)x45 = $2.025 million 40 30 R2 Profit for firm 2 is (75 - 30)x25 = $1.35 million q1 30 40 60 120 45 Industrial Organization: Chapter 7

  12. The Incentive to Cheat (cont.) Both firms have the incentive to cheat on their agreement Firm 2 can make the same calculations! This gives the following pay-off matrix: Firm 1 Cooperate (M) Deviate (D) This is the Nash equilibrium Cooperate (M) (1.8, 1.8) (1.35, 2.025) Firm 2 (1.6, 1.6) Deviate (D) (2.035, 1.35) (1.6, 1.6) Industrial Organization: Chapter 7

  13. Cartel Stability • The cartel in our example is unstable • This instability is quite general • Can we find mechanisms that give stable cartels? • violence in one possibility! • are there others? • must take away the temptation to cheat • staying in the cartel must be in a firm’s self-interest • Suppose that the firms interact over time • Then it might be possible to sustain the cartel • Make cheating unprofitable • Reward “good” behavior • Punish “bad” behavior Industrial Organization: Chapter 7

  14. Repeated Games • Formalizing these ideas leads to repeated games • a firm’s strategy is conditional on previous strategies played by the firm and its rivals • In the example: cheating gives $2.025 million once • But then the cartel fails, giving profits of $1.6 million per period • Without cheating profits would have been $1.8 million per period • So cheating might not actually pay • Repeated games can become very complex • strategies are needed for every possible history • But some “rules of the game” reduce this complexity • Nash equilibrium reduces the strategy space considerably • Consider two examples Industrial Organization: Chapter 7

  15. Example 1: Cournot duopoly The pay-off matrix from the simple Cournot game Firm 1 Cooperate (M) Deviate (D) Cooperate (M) (1.8, 1.8) (1.35, 2.025) Firm 2 (1.6, 1.6) Deviate (D) (2.025, 1.35) (1.6, 1.6) Industrial Organization: Chapter 7

  16. Example 2: A Bertrand Game Firm 1 $105 $130 $160 (7.3125, 7.3125) (7.3125, 7.3125) (8.25, 7.25) (9.375, 5.525) $105 (8.5, 8.5) $130 (7.25, 8.25) (8.5, 8.5) (10, 7.15) Firm 2 $160 (5.525, 9.375) (7.15, 10) (9.1, 9.1) Industrial Organization: Chapter 7

  17. Repeated Games (cont.) • Time “matters” in a repeated game • is the game finite? T is known in advance • Exhaustible resource • Patent • Managerial context • or infinite? • this is an analog for T not being known: each time the game is played there is a chance that it will be played again Industrial Organization: Chapter 7

  18. Repeated Games (cont.) • Take a finite game: Example 1 played twice • A potential strategy is: • I will cooperate in period 1 • In period 2 I will cooperate so long as you cooperated in period 1 • Otherwise I will defect from our agreement • This strategy lacks credibility • neither firm can credibly commit to cooperation in period 2 • so the promise is worthless • The only equilibrium is to deviate in both periods Industrial Organization: Chapter 7

  19. Repeated Games (cont.) • What if T is “large” but finite and known? • suppose that the game has a unique Nash equilibrium • the only credible outcome in the final period is this equilibrium • but then the second last period is effectively the last period • the Nash equilibrium will be played then • but then the third last period is effectively the last period • the Nash equilibrium will be played then • and so on • The possibility of cooperation disappears • The Selten Theorem: If a game with a unique Nash equilibrium is played finitely many times, its solution is that Nash equilibrium played every time. • Example 1 is such a case Industrial Organization: Chapter 7

  20. Repeated Games (cont.) • How to resolve this? Two restrictions • Uniqueness of the Nash equilibrium • Finite play • What if the equilibrium is not unique? • Example 2 • A “good” Nash equilibrium ($130, $130) • A “bad” Nash equilibrium ($105, $105) • Both firms would like ($160, $160) • Now there is a possibility of rewarding “good” behavior • If you cooperate in the early periods then I shall ensure that we break to the Nash equilibrium that you like • If you break our agreement then I shall ensure that we break to the Nash equilibrium that you do not like Industrial Organization: Chapter 7

  21. A finitely repeated game • Assume that the discount rate is zero (for simplicity) • Assume also that the firms interact twice • Suggest a cartel in the first period and “good” Nash in the second • Set price of $160 in period 1 and $130 in period 2 • Present value of profit from this behavior is: • PV2(p1) = $9.1 + $8.5 = $17.6 million • PV2(p2) = $9.1 + $8.5 = $17.6 million • What credible strategy supports this equilibrium? • First period: set a price of $160 • Second period: If history from period 1 is ($160, $160) set price of $130, otherwise set price of $105. Industrial Organization: Chapter 7

  22. A finitely repeated game • These strategies reflect historical dependence • each firm’s second period action depends on the history of play • Is this really a Nash subgame perfect equilibrium? • show that the strategy is a best response for each player Industrial Organization: Chapter 7

  23. A finitely repeated game • This is obvious in the final period • the strategy combination is a Nash equilibrium • neither firm can improve on this • What about the first period? • why doesn’t one firm, say firm 2, try to improve its profits by setting a price of $130 in the first period? Defection does not pay in this case! • Consider the impact • History into period 2 is ($160, $130) • Firm 1 then sets price $105 • Firm 2’s best response is also $105: Nash equilibrium • Profit therefore is PV2(p1) = $10 + $7.3125 = $17.3125 million • This is less than profit from cooperating in period 1 Industrial Organization: Chapter 7

  24. A finitely repeated game • Defection does not pay! • The same applies to firm 1 • So we have credible strategies that partially support the cartel • Extensions • More than two periods • Same argument shows that the cartel can be sustained for all but the final period: strategy • In period t < T set price of $160 if history through t – 1 has been ($160, $160) otherwise set price $105 in this and all subsequent periods • In period T set price of $130 if the history through T – 1 has been ($160, $160) otherwise set price $105 • Discounting Industrial Organization: Chapter 7

  25. A finitely repeated game • Suppose that the discount factor R < 1 • Reward to “good” behavior is reduced • PVc(p1) = $9.1 + $8.5R • Profit from undercutting in period 1 is • PVd(p1) = $10 + $7.3125R • For the cartel to hold in period 1 we require R > 0.756 (discount rate of less than 32 percent) • Discount factors less than 1 impose constraints on cartel stability • But these constraints are weaker if there are more periods in which the firms interact Industrial Organization: Chapter 7

  26. A finitely repeated game • Suppose that R < 0.756 but that the firms interact over three periods. • Consider the strategy • First period: set price $160 • Second and third periods: set price of $130 if the history from the first period is ($160, $160), otherwise set price of $105 • Cartel lasts only one period but this is better than nothing if sustainable • Is the cartel sustainable? Industrial Organization: Chapter 7

  27. A finitely repeated game • Profit from the agreement • PVc(p1) = $9.1 + $8.5R + $8.5R2 • Profit from cheating in period 1 • PVd(p1) = $10 + $7.3125R + $7.3125R2 • The cartel is stable in period 1 ifR > 0.504 (discount rate of less than 98.5 percent) Industrial Organization: Chapter 7

  28. Cartel Stability (cont.) • The intuition is simple enough • suppose the Nash equilibrium is not unique • some equilibria will be “good” and some “bad” for the firms • with a finite future the cartel will inevitably break down • but there is the possibility of credibly rewarding good behavior and credibly punishing bad behavior • make a credible commitment to the good equilibrium if rivals have cooperated • to the bad equilibrium if they have not. Industrial Organization: Chapter 7

  29. Cartel Stability (cont.) • Cartel stability is possible even if cooperation is over a finite period of time • if there is a credible reward system • which requires that the Nash equilibrium is not unique • This is a limited scenario • What happens if we remove the “finiteness” property? • Suppose the cartel expects to last indefinitely • equivalent to assuming that the last period is unknown • in every period there is a finite probability that competition will continue • now there is no definite end period • so it is possible that the cartel can be sustained indefinitely Industrial Organization: Chapter 7

  30. A Digression: The Discount Factor • How do we evaluate a profit stream over an indefinite time? • Suppose that profits are expected to be p0 today, p1 in period 1, p2 in period 2 … pt in period t • Suppose that in each period there is a probability r that the market will last into the next period • probability of reaching period 1 is r, period 2 is r2, period 3 is r3, …, period t is rt • Then expected profit from period t is rtpt • Assume that the discount factor is R. Then expected profit is • PV(pt) = p0 + Rrp1 + R2r2p2 + R3r3p3 + … + Rtrtpt + … • The effective discount factor is the “probability-adjusted” discount factor G = rR. Industrial Organization: Chapter 7

  31. Cartel Stability (cont.) • Analysis of infinitely or indefinitely repeated games is less complex than it seems • Cartel can be sustained by a trigger strategy • “I will stick by our agreement in the current period so long as you have always stuck by our agreement” • “If you have ever deviated from our agreement I will play a Nash equilibrium strategy forever” Industrial Organization: Chapter 7

  32. Cartel Stability (cont.) • Take example 1 but suppose that there is a probability r in each period that the market will continue: • Cooperation has each firm producing 30 thousand • Nash equilibrium has each firm producing 40 thousand • So the trigger strategy is: • I will produce 30 thousand in the current period if you have produced 30 thousand in every previous period • if you have ever produced more than 30 thousand then I will produce 40 thousand in every period after your deviation • This is a “trigger” strategy because punishment is triggered by deviation of the partner • Does it work? Industrial Organization: Chapter 7

  33. Cartel Stability (cont.) A cartel is more likely to be stable the greater the probability that the market will continue and the lower is the interest rate • Profit from sticking to the agreement is: • PVC = 1.8 + 1.8R + 1.8R2 + … = 1.8/(1 - G) • Profit from deviating from the agreement is: • PVD = 2.025 + 1.6 G + 1.6 G2 + … = 2.025 + 1.6 G /(1 - G) • Sticking to the agreement is better if: • PVC > PVD 1.8 1.6 G this requires: > 2.025 + which requires G = rR> 0.592 1 - G 1 - G if r = 1 we need r < 86%; if r = 0.6 we need r < 13.4% Industrial Organization: Chapter 7

  34. Cartel Stability (cont.) • This is an example of a more general result • Suppose that in each period • profits to a firm from a collusive agreement are pM • profits from deviating from the agreement are pD • profits in the Nash equilibrium are pN • we expect that pD > pM > pN • Cheating on the cartel does not pay so long as: There is always a value of G < 1 for which this equation is satisfied This is the short-run gain from cheating on the cartel This is the long-run loss from cheating on the cartel pD - pM G > 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 (high probability-adjusted discount factor) Industrial Organization: Chapter 7

  35. Cartel Stability (cont.) • What about Example 2? • two possible trigger strategies • price forever at $130 in the event of a deviation from $160 • price forever at $105 in the event of a deviation from $160 • Which? • there are probability-adjusted discount factors for which the first strategy fails but the second works • Simply put, the more severe the punishment the easier it is to sustain a cartel Industrial Organization: Chapter 7

  36. Trigger strategies • Any cartel can be sustained by means of a trigger strategy • prevents destructive competition • But there are some limitations • assumes that punishment can be implemented quickly • deviation noticed quickly • non-deviators agree on punishment • sometimes deviation is is difficult to detect • punishment may take time • but then rewards to deviation are increased • The main principle remains • if the discount rate is low enough then a cartel will be stable provided that punishment occurs within some “reasonable” time Industrial Organization: Chapter 7

  37. Trigger strategies (cont.) • Another objection: a trigger strategy is • harsh • unforgiving • Important if there is any uncertainty in the market • suppose that demand is uncertain A firm in this cartel does not know if a decline in sales is “natural” or caused by cheating Suppose that the agreed price is PC Price There is a possibility that demand may be low Actual sales vary between QL and QH And a possibility that demand may be high This is the expected market demand Expected sales are QE PC DH DL DE Quantity QL QE QH Industrial Organization: Chapter 7

  38. Trigger strategies (cont.) • These objections can be overcome • limit punishment phase to a finite period • take action only if sales fall outside an agreed range • Makes agreement more complex but still feasible • Further limitation • approach is too effective • result of 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. Industrial Organization: Chapter 7

  39. The Folk Theorem • Take example 1. The feasible pay-offs describe the following possibilities p2 $1.8 million to eachfirm may not be sustainable but something less will be Collusion on monopoly gives each firm $1.8 million The Folk Theorem states that any point in this triangle is a potential equilibrium for the repeated game $2.1 If the firms collude perfectly they share $3.6 million $2.0 If the firms compete they each earn $1.6 million $1.8 $1.6 p1 $1.8 $1.5 $1.6 $2.0 $2.1 Industrial Organization: Chapter 7

  40. Stable cartels (cont.) • 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 Industrial Organization: Chapter 7

  41. Cartel Formation • What factors are most conducive to cartel formation? • sufficient profit motive • means by which agreement can be reached and enforced • The potential for monopoly profit • collusion must deliver an increase in profits: this implies • demand is relatively inelastic • restricting output increases prices and profits • entry is restricted • high profits encourage new entry • but new entry dissipates profits (OPEC) • new entry undermines the collusive agreement Industrial Organization: Chapter 7

  42. Cartel formation (cont.) • So there must be means to deter entry • common marketing agency to channel output • consumers must be persuaded of the advantages of the agency • lower search costs • greater security of supply • wider access to sellers • denied access if buy outside the agency (De Beers) • trade association • persuade consumers that the association is in their best interests Industrial Organization: Chapter 7

  43. Cartel formation (cont.) • Costs of reaching a cooperative agreement • even if the potential for additional profits exists, forming a cartel is time-consuming and costly • has to be negotiated • has to be hidden • has to be monitored • There are factors that reduce the costs of cartel formation • small number of firms (recall Selten) • high industry concentration • makes negotiation, monitoring and punishment (if necessary) easier • similarity in production costs • lack of significant product differentiation Industrial Organization: Chapter 7

  44. Cartel formation (cont.) • Similarity in costs • suppose two firms with different costs • if they collude they can attain some point on p*1p*2 p2 If all output is made by firm 2 this is total profit  p*1p*2 is curved because the firms have different costs pm  pmpm has a 450 slope and is tangent to p*1p*2 at M p*2 at M firm 1 has profit p1m and firm 2 p2m C p2C M If all output is made by firm 1 this is total profit p2m assume Cournot equilibrium is at C firm 2 will not agree to collude on M without a side payment from firm 1 p1 p1C p1m p*1 pm Industrial Organization: Chapter 7

  45. Cartel formation (cont.)  with side payments it is possible to collude to somewhere on DE p2 pm  but side payments increase the risk of detection E B  without side payments it is only possible to collude to somewhere on AB p*2 C D p2C M p2m  this type of collusion is difficult and expensive to negotiate: e.g. possibility of misrepresentation of costs A p1 p1C p1m p*1 pm Industrial Organization: Chapter 7

  46. Cartel formation (cont.) • Lack of product differentiation • if products are very different then negotiations are complex • need agreed price/output/market share for each product • monitoring is more complex • Most cartels are found in relatively homogeneous product markets • Or firms have to adopt mechanisms that ease monitoring • basing point pricing Industrial Organization: Chapter 7

  47. Cartel formation (cont.) • Low costs of maintaining a cartel agreement • it is easier to maintain a cartel agreement when there is frequent market interaction between the firms • over time • over spatially separated markets • relates to the discussion of repeated games • less frequent interaction leads to an extended time between cheating, detection and punishment • makes the cartel harder to sustain Industrial Organization: Chapter 7

  48. Cartel formation (cont.) • Stable market conditions • accurate information is essential to maintaining a cartel • makes monitoring easier • unstable markets lead to confused signals • makes collusion “near” to monopoly difficult • uncertainty can be mitigated • trade association • common marketing agency • controls distribution and improves market information • Other conditions make cartel formation easier • detection and punishment should be simple and timely • geographic separation through market sharing is one popular mechanism Industrial Organization: Chapter 7

  49. Cartel formation (cont.) • Other tactics encourage firms to stick by price-fixing agreements • most-favored customer clauses • reduces the temptation to offer lower prices to new customers • meet-the competition clauses • makes detection of cheating very effective Industrial Organization: Chapter 7

  50. 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 Industrial Organization: Chapter 7

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