Industrial Organization or Imperfect Competition Repeated Games and Collusion, Mergers

1. Industrial Organization or Imperfect CompetitionRepeated Games and Collusion, Mergers Univ. Prof. dr. Maarten Janssen University of Vienna Summer semester 2011 Week 11 (June 16,17)

2. Different Issues • What are the incentives to form a cartel? • In a given industry, how many firms will form a cartel if binding agreements can be made? • What makes it that cartel members stay within the cartel? • All three issues will be dealt with separately in three parts

3. 1. Incentives for Collusion

4. Scope for collusion Scope for Collusion with quantity choice Q2 Firm 2’s Profits r1 Q2M Q2* Firm 1’s Profits r2 Q1M Q1* Q1

5. p2 p2B p1 p1B Scope for Collusion under price setting R1(p2) Scope for colusion R2 (p1)

6. 2. How many firms will form a cartel?

7. Not an obvious answer • N=2, answer is clear • General N, less obvious • A noncartel firm benefits from cartel as cartel internalizes externality • Output reduction in case of Cournot • Price increases in case of (differentiated) Bertrand • Cartel members have to share the cartel profits among themselves; the more there are, the less for each member

8. Consider the question in Cournot context with cartel as market leader • P = 1 – Q; no cost • N firms in industry, n firms in cartel • Individual profit of a firm not belonging to cartel: (1 – nqc – (N-n)q)q, where qc (q) is output individual cartel (noncartel) member • Individual reaction noncartel firm: 1 – nqc – (N-n-1)q - 2q = 0, or q = (1 – nqc)/(N-n+1) • Given this reaction cartel maximizes (1 – nqc)qc/(N-n+1) wrt qc or qc = 1/2n • Individual output noncartel firm: q = 1/2(N-n+1)

9. How many firms in Cournot setting II • Profits of cartel and noncartel firms: • Cartel members πc(n): 1/4n(N-n+1) • Others π(n): 1/4(N-n+1)2 • Firms want to join cartel as long as this yield more profits, i.e., when π(n) < πc(n+1) • 1/(N-n+1)2 < 1/(n+1)(N-n) • Firms want quit the cartel as long as this yield more profits, i.e., when π(n-1) > πc(n) • 1/(N-n+2)2 > 1/n(N-n+1) • For example when N = 10, cartel with 6 members is stable. • Non-cartel members also benefit from cartel and stability requires their profits to be very similar to that of cartel members!

10. 3. Why stick to the cartel agreement?

11. Collusion Refers to firm conduct intended to coordinate the actions of other firms in the industry Two problems associated: Agreement must be reached Firms must find mechanisms to enforce the agreement

12. Types of collusion • Cartel agreements: an ‘institutional’ form of collusion (also called explicit collusion or secret agreements) • Unlawful (Sherman Act and Art. 85 Treaty of Rome) • Requires evidence of communication • Tacit or Implicit collusion: attained because firms interact often and ‘find’ ‘natural’ focal points. • This second type make things complicated for antitrust authorities • Focus on latter

13. Example of collusion General Mills Kellogg’s

14. Can collusion work if firms play the game each year, forever? • Consider the following “trigger strategy” by each firm: • “Don’t advertise, provided the rival has not advertised in the past. If the rival ever advertises, “punish” it by engaging in a high level of advertising forever after.” • In effect, each firm agrees to “cooperate” so long as the rival hasn’t “cheated” in the past. “Cheating” triggers punishment in all future periods.

15. General Mills Kellogg’s Suppose General Mills adopts this trigger strategy. Kellogg’s profits? Cooperate = 12 +12/(1+i) + 12/(1+i)2 + 12/(1+i)3 + … = 12 + 12/i Value of a perpetuity of $12 paid at the end of every year Cheat = 20 +2/(1+i) + 2/(1+i)2 + 2/(1+i)3 + = 20 + 2/i

16. Kellogg’s Gain to Cheating: • Cheat - Cooperate = 20 + 2/i - (12 + 12/i) = 8 - 10/i • Suppose i = .05 • Cheat - Cooperate = 8 - 10/.05 = 8 - 200 = -192 • It doesn’t pay to deviate. • Collusion is a Nash equilibrium in the infinitely repeated game! General Mills Kellogg’s

17. Benefits & Costs of Cheating • Cheat - Cooperate = 8 - 10/i • 8 = Immediate Benefit (20 - 12 today) • 10/i = PV of Future Cost (12 - 2 forever after) • If Immediate Benefit > PV of Future Cost • Pays to “cheat”. • If Immediate Benefit PV of Future Cost • Doesn’t pay to “cheat”. General Mills Kellogg’s

18. Key Insight • Collusion can be sustained as a Nash equilibrium when there is no certain “end” to a game. • Doing so requires: • Ability to monitor actions of rivals • Ability (and reputation for) punishing defectors • Low interest rate • High probability of future interaction

19. Collusion in Cournot and/or Bertrand • Πi(si,s-i) firm’s profit given strategies of all firms • Πi* = Πi(s*i,s*-i) static Nash equilibrium profits • There are strategies s’i,s’-i s.t. Πi’ = Πi(s’i,s’-i) ≥ Πi(s*i,s*-i), usually leading to higher prices and lower consumer benefits • Can these strategies be sustained in an infinitely repeated game? • Trigger strategies: do your part of the combination (s’i,s’-i) as long as all other players do so, otherwise refer forever after to your part of (s*i,s*-i) • Alternatively, tit-for-tat

20. Equilibrium condition • π is best possible static deviation pay-off • Equilibrium condition: Πi’/(1-δ) ≥ π + δΠi*/(1-δ) if everyone has the same discount factor • Alternatively δ ≥ (π - Πi’)/(π - Πi*). • Generally depends on N: the more firms the more stringent the requirement on δ.

21. Collusion is more likely with fewer firms in homogeneous product markets with more symmetric firms in markets with no capacity constraints in very transparent markets (cheating is seen easily) no hidden discounts no random demand; low demand can be because of cheating others or because of low realization of demand observability lags; if you can get cheating pay-off for more than 1 period equilibrium condition becomes: Πi’/(1-δ) ≥ (1+δ) π + δ2Πi*/(1-δ) or δ ≥ {(π - Πi’)/(π - Πi*)}1/2.

22. 2. Mergers Horizontal: rivals operate in the same market Boeing and McDonell Douglas Continent and Pryca Vertical: firms with buyer-seller relationships Cleveland-Cliffs Iron and Detroit Steel Corporation Conglomerates: mergers other than horizontal an vertical Pepsico and Pizza Hut

23. Merger Paradox • Consider a linear Cournot model with demand P = a-bQ and marginal cost c • Cournot-eq output levels q =(a-c)/b(N+1) and profits (a-c)2/b(N+1)2 • If two firms merge their profits change from 2(a-c)2/b(N+1)2 to (a-c)2/bN2 • Profits are larger after the merger iff 2N2 < (N+1)2 or 1+2N-N2 > 0, which is only the case for N=2. • Merger to Monopoly is profitable; others not! • Other firms benefit from merger!

24. Incentives to merge under product differentiated Bertrand • Demand Dj = 1/n + pj - pj , where pj is average price competitors; no cost • Before merger price setting results in eq with pj = 1/n. • After a merger of two firms, profit of merged firm equals pf1[1/n + ({(n-2)p-f+pf2}/(n-1))- pf1 ] for the first product with similar expression for second, • where pfi is price of i’th product of merged firm • where p-f is price of product of other firm

25. Incentives to merge under product differentiated Bertrand II • First-order condition gives • 1/n + ({(n-2)p-f+2pf2}/(n-1)) - 2pf1 = 0 • Symmetry gives • pf1 = pf2 = pf = ½ [(n-1)/n(n-2) + p-f] • First-order condition non-merging firms • P-f = ½ [1/n + (2pf + (n-3)p-f)/(n-2)] • Equilibrium values • p*f = (n-1)(2n-1)/2n2(n-2) and p*-f = (n-1)2/n2(n-2) • Both values are larger than 1/n: prices increase! • Profits merging firms increase

26. Merger paradox dependent on strategic interaction • Under Cournot, other firms expand output in reaction to merger and therefore profits decline • Under Bertrand, other firms increase prices in reaction to merger and therefore profits increase

27. Benefits and costs of HM Costs: anti-competitive effects reductions of # competitors, greater market power easier coordination (collusion) Benefits: socially beneficial cost savings, increased production efficiency complementary capabilities and assets cost synergies

28. Safe 1800 Post-Merger HI Safe Safe 1000 Safe Safe Safe 50 100 Increase in Herfindhal Index Merger Guidelines Safe Harbours for Mergers under the 1992 Merger Guidelines

29. Benefits and costs of HM Williamson: “only a small cost saving may offset the detrimental effects of a merger” Price Demand Efficiency losses p1 p0 MC0 MC1 Efficiency gains q1 Quantity q0 q0 MR

30. Illustrating Williamson remark ΔMC/MC %-cost reduction sufficient to offset %-price increases for selected ε-values

31. Problems with the efficiency defense of mergers • Firms may try to influence authority’s estimations of the efficiency gains (rent-seeking) • Can these efficiency gains be achieved by other means? • Ignores the reaction of non-merging firms • effects also depend on which firms merge (which costs they have)

32. Indeed, once 2 and 3 take into account the reaction of firm 1, they would not want to merge. Even without efficiency gains a merger may increase welfare! Pre-Merger Market: 3 firms, homogeneous product, Cournot competitionP=1-(q1+q2+q3) c1=0.1; c2=0.3; c3=0.3Post-Merger: Firms 2 and 3 merge

33. Even with efficiency gains a merger may decrease welfare! Pre-Merger Market: 3 firms, homogeneous product, Cournot competitionP=1-(q1+q2+q3) c1=0.01; c2=0.05; c3=0.1Post-Merger Market: Firms 2 and 3 mergeand cost is 0.05