Industrial Organization Lecture 6: Dynamic Oligopoly and Collusion

Transcription

1 Industrial Organization Lecture 6: Dynamic Oligopoly and Collusion Nicolas Schutz Nicolas Schutz Collusion 1 / 49

2 Collusion What is collusion? Nicolas Schutz Collusion 2 / 49

3 Collusion What is collusion? Under oligopolistic competition, a firm s price or quantity decision affects its rivals profits. Put differently, firms actions generate competitive externalities. We say that firms collude when they agree on a profile of prices / quantities which alleviates these externalities. Firms may also collude on other strategic variables, such as investment or advertising. Collusion is illegal in the USA and in the European Union So how do you enforce a collusive agreement? You can t show the collusive contract to a judge... Nicolas Schutz Collusion 2 / 49

4 Collusion What is collusion? Under oligopolistic competition, a firm s price or quantity decision affects its rivals profits. Put differently, firms actions generate competitive externalities. We say that firms collude when they agree on a profile of prices / quantities which alleviates these externalities. Firms may also collude on other strategic variables, such as investment or advertising. Collusion is illegal in the USA and in the European Union So how do you enforce a collusive agreement? You can t show the collusive contract to a judge... Threat of price wars. Try to explain the Bertrand model to an MBA student. Violence. Recent example: The garbage-hauling business in NYC in the 1990 s. We will focus on the first solution. Nicolas Schutz Collusion 2 / 49

5 Collusion Examples: Organization of the Petroleum Exporting Countries (OPEC): a legal cartel. The diamond cartel, organized by De Beers (until 2000). Vitamins market (about $ 800 million fine). Graphite electrodes market (about $250 million fine). Citric acid market (about $ 180 million fine). French mobile telephony market (about 500 million fine). and in many other industries... Nicolas Schutz Collusion 3 / 49

6 Collusion Basic intuition for collusion: If I cut prices today, My rivals will react by cutting prices tomorrow, And the market price will end up close to marginal cost. Question: Does this work? If yes, what are the determinants that facilitate collusion? In the previous lectures, the models were static (at most two periods). To formalize the threat of retaliation, we need to build a dynamic model. Nicolas Schutz Collusion 4 / 49

7 Collusion in Cournot Oligopoly Start with the one-shot Cournot duopoly model. Firms set their quantities simultaneously, and have the same constant unit cost, which we normalize to zero. Market demand is given by p = 1 Q. Nicolas Schutz Collusion 5 / 49

8 Collusion in Cournot Oligopoly Start with the one-shot Cournot duopoly model. Firms set their quantities simultaneously, and have the same constant unit cost, which we normalize to zero. Market demand is given by p = 1 Q. What is the non-cooperative outcome? Since it s a one-shot game, Nash equilibrium seems to be a good solution for this non-cooperative setting. Derive best responses: R i (q j ) = 1 q j 2. Solve for Nash equilibrium quantities: q 1 = q 2 = 1/3, Q = 2/3 and P = 1/3. Firms profits: π 1 = π 2 = 1/9. Nicolas Schutz Collusion 5 / 49

9 Collusion in Cournot Oligopoly What would be the best cooperative (= collusive) outcome? If they cooperate, firms should try to maximize their joint profits: max q 1,q 2 P(q 1 + q 2 )(q 1 + q 2 ) Since firms are identical, assume that they produce the same quantities, i.e., q 1 = q 2 = Q/2. Then, the problem becomes: which is the monopoly problem. max P(Q)Q, Q Equate marginal revenue (1 2Q) and marginal cost (0). Q = 1/2 = 2q i, P = 1/2, and both firms earn π i = 1/8 > 1/9. Nicolas Schutz Collusion 6 / 49

10 Collusion in Cournot Oligopoly Is the collusive outcome sustainable in the one-shot game? Nicolas Schutz Collusion 7 / 49

11 Collusion in Cournot Oligopoly Is the collusive outcome sustainable in the one-shot game? No, it s not a Nash equilibrium. We have just found that the only Nash equilibrium is different from the cooperative outcome. Sanity check: Assume firm 1 sets the cooperative quantity, i.e., q 1 = 1/4. Does firm 2 want to set q 2 = 1/4 as well? Firm 2 solves max q2 q 2 (1 1/4 q 2 ). Differentiate wrt q 2 : 3/4 2q 2 = 0, i.e., q 2 = 3/8 > 1/4. As in the prisoner s dilemma, firms always want to deviate from the collusive outcome in this one-shot game. Nicolas Schutz Collusion 7 / 49

12 Collusion in Cournot Oligopoly In the one-shot Cournot game, there is no scope for collusion: If a firm deviates from the cooperative agreement, there is no way to punish that firm. To allow for retaliation, assume that firms interact repeatedly in the market. More precisely, assume firms play the Cournot game for T + 1 periods (T 0). At each period 0 t T, firms set their quantities non-cooperatively. Firms choose their strategies so as to maximize the sum of their discounted profits: T δ t π i t, where δ is the discount factor, and π i t is firm i s profit in period t. t=0 As usual, we need an equilibrium concept. To rule out non-credible threats, we look for the subgame-perfect equilibria of this multi-stage game. Is cooperation sustainable (as a subgame-perfect equilibrium) in this finitely repeated game? Nicolas Schutz Collusion 8 / 49

13 Collusion in Cournot Oligopoly In the one-shot Cournot game, there is no scope for collusion: If a firm deviates from the cooperative agreement, there is no way to punish that firm. To allow for retaliation, assume that firms interact repeatedly in the market. More precisely, assume firms play the Cournot game for T + 1 periods (T 0). At each period 0 t T, firms set their quantities non-cooperatively. Firms choose their strategies so as to maximize the sum of their discounted profits: T δ t π i t, where δ is the discount factor, and π i t is firm i s profit in period t. t=0 As usual, we need an equilibrium concept. To rule out non-credible threats, we look for the subgame-perfect equilibria of this multi-stage game. Is cooperation sustainable (as a subgame-perfect equilibrium) in this finitely repeated game? No Nicolas Schutz Collusion 8 / 49

14 Collusion in Cournot Oligopoly To see this, let s reason by backward induction (we can do this, because there is a finite number of periods): Start with period T: firms know that the world ends tomorrow, so there is no threat of retaliation if somebody behaves badly. From the firms point of view, in period T, the problem is exactly the same as in the one-shot Cournot game. At time T, they should therefore play the only Nash equilibrium of the one-shot game, i.e., q i = 1/3. Consider time T 1. Firms anticipate that, whatever they do today, the non-cooperative outcome will be played tomorrow. Again, there is no threat of retaliation. Again, firms should play the non-cooperative outcome in period T 1. By induction, this implies that the non-cooperative outcome will be played at each period. Nicolas Schutz Collusion 9 / 49

15 Collusion in Cournot Oligopoly Conclusion: collusion is not sustainable in the finitely repeated Cournot oligopoly model. Actually, there is a much stronger result: Take a normal-form game that has a unique Nash equilibrium, and repeat it T + 1 times. Then, the only subgame-perfect equilibrium of the repeated game is the Nash equilibrium of the one-shot game (repeated T + 1 times). Nicolas Schutz Collusion 10 / 49

16 Collusion in Cournot Oligopoly Now, assume that the Cournot game is played for an infinite number of periods. As before, firms maximize + t=0 δ t π i t. As it turns out, this game can have a very large number of subgame-perfect equilibria. We restrict attention to simple strategies, which we call trigger strategies. Denote by q NC = 1/3 and q C = 1/4 the non-cooperative and collusive quantities, respectively. Denote by π NC and π C the corresponding profits. We say that firm i plays a trigger strategy if: q 0 i = q C, i.e., firm i sets the collusive quantity in stage 0. For all t 1: If q τ = q τ = q i j C for all τ < t, then q t = q i C. Else, q t = q i NC Nicolas Schutz Collusion 11 / 49

17 Collusion in Cournot Oligopoly In words: Firm i sets the cooperative quantity as long as its rival does the same. If its rival deviates once, then, firm i pulls the trigger, and punishes firm j by playing the non-cooperative strategy forever. Nicolas Schutz Collusion 12 / 49

18 Collusion in Cournot Oligopoly In words: Firm i sets the cooperative quantity as long as its rival does the same. If its rival deviates once, then, firm i pulls the trigger, and punishes firm j by playing the non-cooperative strategy forever. We want to prove the following proposition: Proposition There exists δ such that the outcome where both firms play their trigger strategies is a subgame-perfect equilibrium if, and only if, δ δ. Remark: There is an infinite number of periods, so we cannot use backward induction here. Remember than an outcome is a subgame-perfect equilibrium if it induces a Nash equilibrium in every subgame of the original game. Assume that firm 2 is playing its trigger strategy, and let us check whether, in every subgame, firm 1 s best response is to play its trigger strategy. Nicolas Schutz Collusion 12 / 49

19 Collusion in Cournot Oligopoly Given that firm 2 is playing its trigger strategy, there are two types of subgames: 1 Subgames starting at date t, where one of the firms deviated at some date t < t. 2 Subgames starting at date t, where no deviation took place before t. Nicolas Schutz Collusion 13 / 49

20 Collusion in Cournot Oligopoly Given that firm 2 is playing its trigger strategy, there are two types of subgames: 1 Subgames starting at date t, where one of the firms deviated at some date t < t. 2 Subgames starting at date t, where no deviation took place before t. Consider type 1 subgames: Since firm 2 is playing its trigger strategy, we know that it will set quantity q NC forever. At each period, the best thing firm 1 can do is set q NC as well. This is actually part of firm 1 s trigger strategy. The outcome where both firms play their trigger strategies is indeed a Nash equilibrium of type 1 subgames. Nicolas Schutz Collusion 13 / 49

21 Collusion in Cournot Oligopoly Now, consider type 2 subgames (starting at time t): Since nobody cheated before, and since firm 2 is playing its trigger strategy, firm 2 will set q C in period t. What would be the best deviation possible for firm 1? If firm 1 wants to deviate, the best thing it can do is set q 1 = R 1 (q C ) = 3/8 at time t. In this case, firm 1 earns π D = (3/8) 2 at time t. In all subsequent periods, firm 2 pulls the trigger and sets q NC. Firm 1 should then best-respond by setting q NC as well. Firm 1 earns π NC = 1/9 in periods τ t + 1. If firm 1 deviates, it gets at most π D + + τ=t+1 δτ t π NC. Nicolas Schutz Collusion 14 / 49

22 Collusion in Cournot Oligopoly Type 2 subgames (Cont d): If firm 1 does not deviate, it gets + τ=t δ τ t π C. Therefore, firm 1 does not want to deviate if, and only if, π D + This concludes the proof. + τ=t+1 δ τ t π NC δ 1 δ + τ=t δ τ t π C δ 8 δ δ 9 17 Nicolas Schutz Collusion 15 / 49

23 Collusion in Cournot Oligopoly Comments: We call δ the critical discount factor. We will say that a parameter facilitates collusion if it decreases the critical discount factor. If firms are patient enough, collusion is feasible in Cournot oligopolies. Intuitively, when firms decide whether to deviate from the collusive outcome, they face the following trade-off: Deviating today enables to capture more short-run profits (at the expense of the rival) but induce an infinite punishment tomorrow. If firms care a lot about the future (high δ), the second effect dominates, and collusion is self-enforceable. Nicolas Schutz Collusion 16 / 49

24 Collusion in Bertrand Oligopoly Now assume that firms compete in prices. Denote by Q(p) the total demand. Consider the one-shot game: What is the best cooperative outcome? Both firms should set price p m, where p m solves arg max p (p c)q(p). Then, each firm earns π C = πm 2, where πm (p m c)q(p m ) is the monopoly profit. If a firm deviates from the cooperative outcome, how much profit does it get? Best deviation: Set p = p m ε, where ε 0. π D = π m. What is the non-cooperative outcome? As usual, it s the one-shot Nash equilibrium: p 1 = p 2 = c. π NC = 0. Nicolas Schutz Collusion 17 / 49

25 Collusion in Bertrand Oligopoly Now consider the infinitely repeated game: Firms maximize the sum of their discounted profits: t=0 δ t π i t. As before, define the trigger strategies. For i = 1, 2, t 1: If t = 0, then, p i t = pm. If t > 0 and p i τ = p j τ = p m for all τ < t, then, p i t = pm. Else, p i t = c. Nicolas Schutz Collusion 18 / 49

26 Collusion in Bertrand Oligopoly Can the outcome where both firms play their trigger strategies be a subgameperfect equilibrium? Assume that firm 2 is playing its trigger strategy, and suppose that firm 1 set price p m in all periods up to stage t. Then, firm 2 sets p m in stage t. Best deviation possible for firm 1: set p m ε and earn π D in period t, and set p 1 = c in all subsequent periods. For collusion to be an equilibrium, this deviation should not be profitable: π D + δ τ t π NC τ=t+1 δ τ t π C τ=t π m π m 1 δ 2 δ δ 1 2 Nicolas Schutz Collusion 19 / 49

27 Collusion in Bertrand Oligopoly It is then straightforward to show that, in all other subgames (i.e., subgames where firm 2 sets p 2 = c forever), it is also a best-response for firm 1 to play its trigger strategy (i.e., here, set p 1 = c forever). Conclusion: Collusion is a subgame-perfect equilibrium (in trigger strategies) iff δ 1 2. Again, firms manage to collude if they are patient enough. Nicolas Schutz Collusion 20 / 49

28 Determinants of Collusion The number of firms has a direct impact on the feasibility of collusion. Assume there are N firms competing à la Bertrand. The collusive payoff becomes πm N, whereas the deviation profit and the noncooperative profit remain π m and 0 respectively. The incentive compatibility constraint (or non-deviation constraint) in period 1 becomes: π m + δ t 0 t=1 t=0 δ t πm N δ δ (N) 1 1 N δ (N) increases in N, i.e., collusion is more difficult to sustain with more firms. Intuition? Nicolas Schutz Collusion 21 / 49

29 Determinants of Collusion The number of firms has a direct impact on the feasibility of collusion. Assume there are N firms competing à la Bertrand. The collusive payoff becomes πm N, whereas the deviation profit and the noncooperative profit remain π m and 0 respectively. The incentive compatibility constraint (or non-deviation constraint) in period 1 becomes: π m + δ t 0 t=1 t=0 δ t πm N δ δ (N) 1 1 N δ (N) increases in N, i.e., collusion is more difficult to sustain with more firms. Intuition? Higher N reduces the collusive profit increases the incentives to deviate from collusion. Nicolas Schutz Collusion 21 / 49

30 Determinants of Collusion Other reasons why more firms may make collusion less likely: Reaching a collusive agreement becomes harder when the number of participants increase. In our simple model, firms are symmetric, so it makes sense to give 1 N of the collusive profit to each firm. With asymmetric firms, the way the surplus should be shared becomes less obvious. Each firm may feel entitled to a high share of the surplus. This can make the negotiation process much harder. The likelihood that the competition authority eventually detects the cartel increases in N. Deviations from the collusive outcome become harder to monitor with higher N. Nicolas Schutz Collusion 22 / 49

31 Determinants of Collusion Another determinant of collusion: Market growth. Let s go back to the two-firm case. Assume now that demand at time t is given by Q t (p) = A t Q(p), where A > 0. The collusive profit becomes π C (t) = 1 2 At π m (= 1 2 max p(p c)a t Q(p)). The deviation profit is π D (t) = A t π m. We still have π NC = 0. Incentive-compatibility constraint at time t (w/ trigger strategies): δ t A t π m + 0 τ=t δ τ A τ πm 2 δ δ 1 2A Collusion is easier in an expanding market (A > 1) / harder in a shrinking market (A < 1). Nicolas Schutz Collusion 23 / 49

32 Determinants of Collusion Which discount factor should we use? Some assumptions: The firm s stock is publicly traded. Denote by P t the price of a share at time t. Denote by n the number of shares. At each period, the firm redistributes all its profits to its shareholders. Denote also by r the interest rate (say, on treasury bonds) between time t and time t + 1, and assume it is constant over time. Assume you have P t dollars at time t. Then, you should be indifferent between investing these dollars in stocks and purchasing bonds: If you purchase 1 share of the firm s stock at time t, and sell it at time t + 1, your income at time t + 1 is P t+1 + π t n. If you purchase P t bonds at time t, your income at time t + 1 is P t (1 + r). Nicolas Schutz Collusion 24 / 49

33 Determinants of Collusion This yields the non-arbitrage condition: P t+1 + π t n = P t(1 + r) P t = π t/n 1 + r + P t r Notice that this relation has to hold for all t. This system of equations can have several solutions. We impose that stock prices do not explode as t increases: lim t = 0 (no-bubble condition). P t (1+r) t P t = π t/n 1 + r + P t r = π t/n 1 + r r (π t+1/n 1 + r + P t r ) = π t/n 1 + r + π t+1/n (1 + r) + P t+2 2 (1 + r) 2 =... = T τ=t π τ /n (1 + r) τ t+1 + P T (1 + r) T t Nicolas Schutz Collusion 25 / 49

34 Determinants of Collusion Now, take the limit as T goes to infinity, and use the non-bubble condition: P t = 1 1 n 1 + r τ=t π τ (1 + r) τ t Since firms maximize the value of their stock prices, the relevant discount factor is 1/(1 + r). Now, denote by r y the yearly interest rate. Assume that firms change their prices f times per year, so that the length of a period is 1/f -th of a year. In this case, the relevant interest rate is r ry f. Therefore, in a two-firm Bertrand duopoly, collusion is possible iff: δ r y /f 1 2 f ry Collusion is easier to sustain if firms can change their prices frequently. Nicolas Schutz Collusion 26 / 49

35 Determinants of Collusion Now, take the limit as T goes to infinity, and use the non-bubble condition: P t = 1 1 n 1 + r τ=t π τ (1 + r) τ t Since firms maximize the value of their stock prices, the relevant discount factor is 1/(1 + r). Now, denote by r y the yearly interest rate. Assume that firms change their prices f times per year, so that the length of a period is 1/f -th of a year. In this case, the relevant interest rate is r ry f. Therefore, in a two-firm Bertrand duopoly, collusion is possible iff: δ r y /f 1 2 f ry Collusion is easier to sustain if firms can change their prices frequently. Intuitively, when firms interact often, they can punish a deviation very quickly. Nicolas Schutz Collusion 26 / 49

36 Determinants of Collusion Collusion is also more difficult to implement when firms are imperfectly informed about their rivals prices. When this is the case, a deviating firm may not be punished, simply because its rivals did not observe the deviation. When prices are not public information, firms may try to exchange information about their respective prices, but: Firms may lie. Even if they find a way to reveal this information truthfully, communication may make the competition authority suspicious. Nicolas Schutz Collusion 27 / 49

37 Determinants of Collusion Collusion is also more difficult to implement when firms are imperfectly informed about their rivals prices. When this is the case, a deviating firm may not be punished, simply because its rivals did not observe the deviation. When prices are not public information, firms may try to exchange information about their respective prices, but: Firms may lie. Even if they find a way to reveal this information truthfully, communication may make the competition authority suspicious. Two simple ways to solve this problem: Meet-the-competition clauses: Your consumers can ask for a price refund if they observe that one of your rivals is charging a lower price. Consumers are involuntarily monitoring collusion! Most-favored-customer clauses: Your past consumers can ask for a price refund if you decrease your price today. As in the durable goods monopolist case, this reduces firms incentives to cut prices. Nicolas Schutz Collusion 27 / 49

38 Determinants of Collusion Collusion and unobservable price cuts (Cont d): Sometimes, misguided government intervention may also (again, involuntarily) help firms to collude: Ready-mixed concrete market in Denmark: Ready-mixed concrete is difficult to transport: There are dozens of heavily concentrated small geographical submarkets. It should not be too difficult to collude. But concrete prices were individually negotiated b/w producers and buyers. Producers were not able to observe price cuts. In Oct. 1993, the Danish competition authority decided to regularly publish transaction prices set by individual firms, in order to increase market transparency. Nicolas Schutz Collusion 28 / 49

39 Determinants of Collusion Prices went up by 15 20% within one year. The Danish Competition Council decided to stop publishing concrete prices in Dec Nicolas Schutz Collusion 29 / 49

40 Determinants of Collusion Collusion with asymmetric firms. Assume firms 1 and 2 have asymmetric costs: c 1 = c < c = c 2. Then, it can be shown that, if δ 1/2, there exist collusive equilibria. These equilibria have the following characteristics: p [p m (c), p m (c)]. Both firms have > 0 market shares. Nicolas Schutz Collusion 30 / 49

41 Determinants of Collusion Several issues: There is no obvious way for firms to choose among these multiple equilibria. When firms are symmetric, it seems reasonable for them to coordinate on the equilibrium where they share the market at the monopoly price. Here, it may be more difficult to choose the collusive price and the market shares. Negotiation may be difficult. Firms may also try to misreport their respective marginal costs. Dissatisfied firms may then start price wars to get a larger share of the cake. The joint-profit maximizing outcome (i.e., p = p m (c), and firm 1 supplies all the market) cannot be implemented in a subgame-perfect equilibrium. Nicolas Schutz Collusion 31 / 49

42 Determinants of Collusion Firms may try to use side-payments to get around these issues: Firm 1 supplies the whole market at price p m (c). Firm 2 sets p 2 =. As long as firm 2 stays out of the market, at each period, firm 1 pays a bribe to firm 2. This outcome maximizes joint profits, but: Again, firms may have a hard time agreeing on the side payment. Side payments may be difficult to hide in company accounts. Competition authorities may not like this. Bottom line: Collusion is harder when firms are asymmetric. Nicolas Schutz Collusion 32 / 49

43 Determinants of Collusion Collusion and multimarket contacts: There are two market, A and B. Q A (p A ) = Q(p A ), Q B (p B ) = Q(p B ). Market A: c A 1 = c < c = ca 2. Market B: c B 2 = c < c = cb 1. Nicolas Schutz Collusion 33 / 49

44 Determinants of Collusion Collusion and multimarket contacts: There are two market, A and B. Q A (p A ) = Q(p A ), Q B (p B ) = Q(p B ). Market A: c A 1 = c < c = ca 2. Market B: c B 2 = c < c = cb 1. Without multimarket contacts (say, if market B does not exist), we know that firms A and B may have a hard time reaching a collusive agreement. Nicolas Schutz Collusion 33 / 49

45 Determinants of Collusion Collusion and multimarket contacts: There are two market, A and B. Q A (p A ) = Q(p A ), Q B (p B ) = Q(p B ). Market A: c A 1 = c < c = ca 2. Market B: c B 2 = c < c = cb 1. Without multimarket contacts (say, if market B does not exist), we know that firms A and B may have a hard time reaching a collusive agreement. With multimarket contacts, consider the following trigger strategies: If t = 0, then p A 1 (t) = pm (c) and p B (t) = +. 1 If t 1: If for all τ < t, p A (τ) = 1 pb(τ) = 2 pm (c) and p B(τ) = 1 pa(τ) =, then, 2 pa(t) = 1 pm (c) and p B (t) = +. 1 Else, p A (t) = c and 1 pb (t) = c + ε. 1 (+ symmetric trigger strategy for firm 2, i.e., p B 2 (t) = pm (c) and p A (t) = + etc) 2 Nicolas Schutz Collusion 33 / 49

46 Determinants of Collusion It is then straightforward to show that these trigger strategies form a subgameperfect equilibrium iff δ 1/2. Put differently, the joint-profit maximizing outcome can be sustained under multimarket contacts. In equilibrium, firm 1 supplies market A at its monopoly price, while firm 2 supplies market B at its monopoly price. Multimarket contacts flatten out asymmetries b/w firms. Multimarket contacts facilitate collusion. Nicolas Schutz Collusion 34 / 49

47 Determinants of Collusion Multimarket contacts: Examples: Chemical industry, 1920s: Collusive agreement among Dupont, ICI and a group of German firms. ICI supplied the UK + Commonwealth countries, German firms = Continental Europe, DuPont = America. Dog food industry, 1980s: In 1986, Quaker Oats acquired Anderson Clayton 81% market share in the moist food market, 20% market share in the dry food market. Ralston Purina (50% market share in the dry food market) responded by acquiring Benco Pet Food Inc., Quaker s main rival in the moist food market. We can come at you in your strong area if you come after us in our strong area. Nicolas Schutz Collusion 35 / 49

48 Price Wars In the models developed so far, price wars never occur: Either firms manage to collude, and the price stays at the collusive level forever. Or they don t, and the price is set at marginal cost forever. In these models, price wars are out-of-equilibrium phenomena. The threat of price wars enable firms to enforce collusion. Nicolas Schutz Collusion 36 / 49

49 Price Wars In the models developed so far, price wars never occur: Either firms manage to collude, and the price stays at the collusive level forever. Or they don t, and the price is set at marginal cost forever. In these models, price wars are out-of-equilibrium phenomena. The threat of price wars enable firms to enforce collusion. Nevertheless, we do observe price wars in reality. happens? Why do you think this Nicolas Schutz Collusion 36 / 49

50 Price Wars In the models developed so far, price wars never occur: Either firms manage to collude, and the price stays at the collusive level forever. Or they don t, and the price is set at marginal cost forever. In these models, price wars are out-of-equilibrium phenomena. The threat of price wars enable firms to enforce collusion. Nevertheless, we do observe price wars in reality. happens? Price wars may be due to unanticipated shocks: Why do you think this For instance, in our simple model of collusive behavior, the entry of a new competitor, or new informations about the future of the industry can raise the critical discount factor. If collusion was feasible before the shock, but not after the shock, then we would observe a price war. Nicolas Schutz Collusion 36 / 49

51 Price Wars Another type of idiosyncratic shock: liquidity shocks. Financially distressed firms may need to make a lot of profits immediately to avoid going bankrupt. [Aside: If credit markets were perfectly competitive, this would never happen: investors would only care about the firm s sum of discounted future profits. They would agree to lend to the firm as long as its net present value is positive. But we know that market failures do occur in credit markets.] A good way to model this: assume that the financially distressed firm s discount factor decreases following the liquidity shock. The firm may then decide to start a price war, to collect as much short-run profits as possible. Firms in worse financial conditions are more likely to start price wars. Nicolas Schutz Collusion 37 / 49

52 Price Wars Financial conditions and price wars: some evidence from the airline industry: CEO of Alaska Airlines: Fares are dictated not by the strongest, but by the financially troubled. Airlines that subsequently went bankrupt have 5% lower prices for several months before bankruptcy. Firms are more likely to start a price war when their leverage (debt to equity ratio) is high. Nicolas Schutz Collusion 38 / 49

53 Price Wars Price wars may also allow some firms to win a distributional battle b/w members of the cartel: Remember the model of collusion with asymmetric marginal costs. It may be difficult for cartel members to reach an agreement on prices, market shares, etc. This can be even harder if side payments are not feasible and if the marginal cost of each firm is not common knowledge. In a bargaining framework with asymmetric information, firms may behave in a way that hurts themselves and their competitors to eventually get a larger share of the cake. Example: Assume some cartel members are financially distressed (i.e., they need to make profits asap), while some others are not. Assume firms do not know which of their rivals are in trouble. It may then be in some firms interest to start a price war: Financially distressed firms will eventually reveal their type, and therefore get a smaller share of the surplus, by pulling out of the price war. Nicolas Schutz Collusion 39 / 49

54 Price Wars Secret price cuts and demand fluctuations: Suppose that at each period t, demand is given by: D(p) 1 µ w/ prob 1 µ, D t (p) = 0 w/ prob µ. If a firm sells nothing, then this comes either from the realization of a demand shock, or from a deviation of its rival. Unobservable shock: impossible to disentangle these two reasons. Firms must take their decisions (prices) before the shock is realized. Expected per-period profit if collusion: π m = E { (p m c)d t (p m ) } = (1 µ)(p m c) D(pm ) 1 µ + µ 0 = (pm c)d(p m ). Nicolas Schutz Collusion 40 / 49

55 Price Wars If firms observe at the end of each period whether a shock has realized or not, then we know that collusion is sustainable if δ 1 2. If firms do not observe the shock: Firms should punish every time they observe low demand. Otherwise, firms would always cheat. But infinite reversion to the Bertrand equilibrium seems too harsh: sooner or later, a demand shock will occur, and the industry would then shift to the Bertrand outcome. Intermediate solution: Move to price war for T periods, then, revert back to collusive pricing. These strategies form a subgame-perfect equilibrium when δ is larger than some threshold δ (T). In this model, price wars are an equilibrium phenomenon which helps discipline the collusive agreement. Nicolas Schutz Collusion 41 / 49

56 Price Wars Example of this kind of price wars: The Joint Executive Committee, a cartel that controlled freight shipment from Chicago to the East Coast in the 1880s. Nicolas Schutz Collusion 42 / 49

57 Price Wars Price wars and observable demand fluctuations: In many circumstances, it may be more realistic to assume that firms observe demand fluctuations. For instance, GDP statistics are public information, and it is quite easy to know whether the economy is in a boom or in a bust. Assume that, at each period, total demand is given by Q t (p) = A t Q(p), where { 1 + ε with probability 1/2 A t = 1 ε with probability 1/2 Assume that A t is observable at the beginning of period t, i.e., before firms set their prices. Suppose first that firms try to collude at the monopoly price p m in every period. [Since the demand shock A t is multiplicative, it does not affect the monopoly price] Nicolas Schutz Collusion 43 / 49

58 Price Wars Assume also that firms use their usual trigger strategies. At each period, the expected industry profit under collusion is just E(Π) = 1 2 (1 + ε)πm (1 ε)πm = π m During booms, the non-deviation constraint is: (1 + ε)π m (1 + ε) πm 2 + δ π m 1 δ 2 Cheating during a boom is not profitable iff δ δ B (ε) = 1+ε 2+ε. Similarly, firms don t want to deviate during slumps iff δ δ S (ε) = 1 ε 2 ε. Notice that δ B (ε) > 1/2 > δ S (ε): Collusion is harder to sustain when the economy is booming. In particular, if δ (δ S (ε), δ B (ε)), this profile of trigger strategies cannot be an equilibrium. Nicolas Schutz Collusion 44 / 49

59 Price Wars Assume that 1/2 < δ < δ B (ε). We know that collusion is not sustainable w/ the usual trigger strategies. Define p, such that p < p m and (1 + ε)(p c)q(p) = (1 ε)π m. Consider the following strategy: Set p m in low-demand states, and p in high-demand states. Set c forever if anybody deviates from the above pricing rule. Assume the current demand state is high, and suppose your rival is using the above strategy profile. You don t want to deviate iff: (1+ε)(p c)q(p) 1 2 (1+ε)(p c)q(p)+ δ t 1 { (1 ε)πm + 1 } 2 (1 + ε)(p c)q(p) t=1 By definition of p, this can be rewritten as: (1 ε) πm 2 δ (1 ε)πm 1 δ 2 Nicolas Schutz Collusion 45 / 49

60 Price Wars Notice that the non-deviation constraint in low-demand states is also (1 ε) πm 2 δ (1 ε)πm 1 δ 2 Therefore, this profile of trigger strategies is a subgame-perfect equilibrium iff δ 1/2. Nicolas Schutz Collusion 46 / 49

61 Price Wars Notice that the non-deviation constraint in low-demand states is also (1 ε) πm 2 δ (1 ε)πm 1 δ 2 Therefore, this profile of trigger strategies is a subgame-perfect equilibrium iff δ 1/2. Summary: When 1/2 < δ < δ B (ε), efficient collusion is not feasible, because firms have strong incentives to deviate during booms. To make high-demand states deviations less attractive, it may be necessary to agree on a lower collusive price (p) during booms. The model predicts that we should observe price wars during booms. This seems to be supported by empirical evidence: in industries where firms are known to collude (e.g., the cement industry), markups tend to be counter-cyclical. Nicolas Schutz Collusion 46 / 49

62 Collusion and Antitrust Collusion has been illegal in the U.S. since the Sherman Act (1890): Section 1: Every contract, combination in the form of trust or otherwise, in restraint of trade or commerce [... ] is declared to be illegal. Section 2: Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce [... ] shall be deemed guilty of a felony [... ] Nicolas Schutz Collusion 47 / 49

63 Collusion and Antitrust Collusion has been illegal in the U.S. since the Sherman Act (1890): Section 1: Every contract, combination in the form of trust or otherwise, in restraint of trade or commerce [... ] is declared to be illegal. Section 2: Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce [... ] shall be deemed guilty of a felony [... ] Collusion is also illegal in the European Union: Article of the Treaty on the Functioning of the European Union: The following shall be prohibited as incompatible with the internal market: all agreements between undertakings, decisions by associations of undertakings and concerted practices which may affect trade between Member States and which have as their object or effect the prevention, restriction or distortion of competition within the internal market, and in particular those which: (a) directly or indirectly fix purchase or selling prices or any other trading conditions; (b) limit or control production [... ] Nicolas Schutz Collusion 47 / 49

64 Collusion and Antitrust Collusion has been illegal in the U.S. since the Sherman Act (1890): Section 1: Every contract, combination in the form of trust or otherwise, in restraint of trade or commerce [... ] is declared to be illegal. Section 2: Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce [... ] shall be deemed guilty of a felony [... ] Collusion is also illegal in the European Union: Article of the Treaty on the Functioning of the European Union: The following shall be prohibited as incompatible with the internal market: all agreements between undertakings, decisions by associations of undertakings and concerted practices which may affect trade between Member States and which have as their object or effect the prevention, restriction or distortion of competition within the internal market, and in particular those which: (a) directly or indirectly fix purchase or selling prices or any other trading conditions; (b) limit or control production [... ] Similar legislation in most other countries. Nicolas Schutz Collusion 47 / 49

65 Collusion and Antitrust Policymakers may be tempted to define collusion as a situation in which prices are above a competitive benchmark, and not as the specific form through which that outcome has been attained. But: Pb 1: Very difficult to implement in practice. Pb 2: The principle that firms could be convicted solely on the grounds that they charge too high a price is dangerous. Bottom line: Inferring illegal collusive behavior from market data is very difficult. The indistinguishability theorem. Assume firm 1 increases its price from p to p. Assume firm 2 quickly reacts by doing the same. Is this evidence of collusion? Not necessarily: maybe firms 1 and 2 were playing the Bertrand outcome before. Maybe an increase in their marginal costs force them to increase their prices. Legal approach requires hard evidence (proof of communication or agreement) that firms have not acted unilaterally. Nicolas Schutz Collusion 48 / 49

66 Collusion and Antitrust Competition policies against collusion: Ex ante: Black list of facilitating practices (announcements about future price and quantity conduct, coordination among firms aimed at harmonizing business practices that increase price observability among sellers (w/o increasing transparency for buyers), etc.). Auction design to avoid bid-rigging. Ex post: Surprise inspections or dawn raids. Leniency programs (total or partial immunity from fines to firms that collaborate w/ authorities). Nicolas Schutz Collusion 49 / 49