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Chapter 7 Collusion and Cartels

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1 Chapter 7 Collusion and Cartels
Industrial Organization: Chapter 7

2 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 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 Industrial Organization: Chapter 7
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 = = $70 R2 Profit to each firm is: q1 p1 = p2 = ( )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 = ( ) = $90 R1 Profit for each firm is: 60 p1 = p2 = ( )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 = 70 thousand Price is PD = = $75 60 C Profit of firm 1 is ( )x45 = $ million 40 30 R2 Profit for firm 2 is ( )x25 = $ 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 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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, ) $105 (7.3125, ) (8.25, 7.25) (9.375, 5.525) (8.5, 8.5) Firm 2 $130 (7.25, 8.25) (8.5, 8.5) (10, 7.15) $160 (5.525, 9.375) (7.15, 10) (9.1, 9.1) Industrial Organization: Chapter 7

17 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 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 Industrial Organization: Chapter 7
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 + $ = $ 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 > (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 < 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 if R > (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 = R + 1.8R2 + … = 1.8/(1 - G) Profit from deviating from the agreement is: PVD = G G 2 + … = G /(1 - G) Sticking to the agreement is better if: PVC > PVD 1.8 1.6 G this requires: > 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 Industrial Organization: Chapter 7
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 each firm 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 $1.5 $1.6 $1.8 $2.0 $2.1 Industrial Organization: Chapter 7

40 Industrial Organization: Chapter 7
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 Industrial Organization: Chapter 7
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 p*2  without side payments it is only possible to collude to somewhere on AB C p2C D M p2m A  this type of collusion is difficult and expensive to negotiate: e.g. possibility of misrepresentation of costs 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

51 Industrial Organization: Chapter 7
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 “the indistinguishability theorem” ICI/Solvay soda ash case accused of market sharing in Europe no market interpenetration despite price differentials defense: price differentials survive because of high transport costs soda ash has rarely been transported so no data on transport costs are available The Cournot model illustrates this “theorem” Industrial Organization: Chapter 7

52 The Indistinguishability Theorem
 start with a standard Cournot model: C is the non-cooperative equilibrium q2 R1  assume that the firms are colluding at M: restricting output  M can be presented as non-collusive if the firms exaggerate their costs or underestimate demand R’1 C  this gives the apparent best response functions R’1 and R’2 M R’2 R2  M now “looks like” the non-cooperative equilibrium q1 Industrial Organization: Chapter 7

53 Industrial Organization: Chapter 7
An Example  Suppose market demand is P = Q, that there are 3 firms and that each firm has true marginal costs of $20  The Cournot equilibrium market price and the outputs for each firm are given by the equations: qi = (A - c)/(N + 1); PC = (A + cN)/(N + 1) where we have that A = 100, c = 20, N = 3  So we have: qi = 20 and PC = $40  Suppose the firms are colluding on the monopoly price, which is (A + c)/2 = $60  What production cost 20 + f would make this look like a Cournot price? We need ( (20 + f))/4 = 60; so f = 240 which gives f = $80/3 = $26.67  The same result can be obtained by overestimating the reservation price Industrial Organization: Chapter 7

54 Cartel detection (cont.)
Cartels have been detected in procurement auctions bidding on public projects; exploration the electrical conspiracy using “phases of the moon” those scheduled to lose tended to submit identical bids but they could randomize on losing bids! Suggested that losing bids tend not to reflect costs correlate losing bids with costs! Is there a way to beat the indistinguishability theorem? Osborne and Pitchik suggest one test Industrial Organization: Chapter 7

55 Industrial Organization: Chapter 7
Testing for collusion Suppose that two firms compete on price but have capacity constraints choose capacities before they form a cartel Then they anticipate competition after capacity choice a collusive agreement will leave the firms with excess capacity uncoordinated capacity choices are unlikely to be equal one firms or the other will overestimate demand so both firms have excess capacity but one has more excess Collusion between the firms then leads to: firm with the smaller capacity making higher profit per unit of capacity this unit profit difference increases when joint capacity increases relative to market demand Industrial Organization: Chapter 7

56 An example: the salt duopoly
British Salt and ICI Weston Point were suspected of operating a cartel BS is the smaller firm and makes more profit per unit of capacity The profit difference grows with capacity 1980 1981 1982 1983 1984 BS Profit 7065 7622 10489 10150 10882 WP Profit 7273 7527 6841 6297 6204 BS profit per unit of capacity 8.6 9.3 12.7 12.3 13.2 WP profit per unit of capacity 6.6 6.9 6.3 5.8 5.7 Total Capacity/Total Sales 1.5 1.7 1.7 1.9 1.9 BS capacity: 824 kilotons; WP capacity: 1095 kilotons But will this test be successful once it is widely known and applied? Industrial Organization: Chapter 7

57 Industrial Organization: Chapter 7

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

59 Birmingham Steel Company
Basing Point Pricing Then it was priced at the mill price plus transport costs from Pittsburgh Pittsburgh Suppose that the steel is made here And that it is sold here Birmingham Steel Company Industrial Organization: Chapter 7

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