2013-14, spring term

1. EC930 Theory ofIndustrial OrganisationCollusion and Cartel stabilityFacilitating Practices(week 6) 2013-14, spring term

2. Outline The incentive to collude and the incentive to deviate Tacit Collusion (more detailed outline to follow in body of presentation) Reading: Lecture Notes 5, 6 Cabral ch 8 Tirolech 6

3. Multiple Choice It is easier for Bertrand competitors to collude than for Cournotcompetitors, all else equal. If firms are attempting to tacitly collude, we should expect prices to move counter-cyclically. Customers do better when firms provide a guarantee to match any competitor’s low price than when such guarantees are not available. d. Firms can achieve tacit collusion easier if they have the ability to change output levels rapidly, all else equal.

4. Collusion: some questions • How can firms sustain collusion? • What is the impact on consumers? • What features of an industry make collusion more, or less, likely to occur (and be sustained)? • How can collusion be detected?

5. Collusion and cartelisation • Defn: Collusion – • Cooperation between firms over price, output, market share, quality, innovation, advertising or territory to achieve higher profits

6. Non-cooperative oligopoly • Cournot oligopoly • n firms each choose qi, treating rivals’ choices as given • Inverse demand P = a – bQ; marginal cost c • Eqm outcomes (from lecture 2) • Outputs ; • Price • Profit • As n  : qiC  0, QC  , pC  c, iC  0

7. Comparing Monopoly and Oligopoly: The Incentive to Collude • Monopoly • Profit where • 1/nth share of monopoly profit • Cournot oligopoly • Profit • Difference • NB: Bertrand (homogenous goods)  = 0

8. Reaching a collusive agreement • Relatively straightforward when • Few firms • Homogeneous goods, similar production costs • Stable industry demand and costs • If products are differentiated • How to decide price (or output level) for each one? • Firms have different costs • Efficient for high cost firms produce less: side payments • Industry shocks • Need to adjust prices: price leadership may help

9. Collusion and cartelisation • At best, collusion achieves monopoly profit (in sum) • Usually worse for consumers, and social welfare • Hence, collusion illegal in most antitrust jurisdictions • In particular, any contract enforcing collusion would be illegal and so unenforceable in court.

10. Collusion and cartelisation Defn: Cartel – • Institutionalised collusion, with explicit agreement between firms (could be verbal) • If there were no incentive to deviate from a cartel agreement, then the fact that explicit contracts not enforceable would not be a problem. • However, there is an incentive to deviate…

11. Can collusion be sustained? • Prisoners’ dilemma: collude or defect? • Bertrand model • Firm that defects just undercuts to take entire m • Defection by both gives Bertrand eqm: p = c;  = 0 • One-shot Nash equilibrium • Both players choose defect • Payoffs 0 each; collusive profits are forfeited

12. The Incentive to Deviate q2 • Collusive outcome not on either of the • reaction functions  incentive to deviate • back to reaction function. • Need some kind of punishment in • order to maintain collusion if firms • behave to maximise own profits • non-cooperatively. RF of firm 1 Cournot Equilibrium • • RF of firm 2 qM/2 qM/2 q1

13. The need for punishment combined with the illegality of explicit collusion leads to: • Tacit collusion: Accommodation reached without formal agreement, (by firms building understanding and trust or • by building tacit reciprocal agreements such as punishments) • Facilitating Practices: Practices that tend to soften competition. • We will study both in this lecture…

14. Repeated games • General discussion of repeated games • Trigger strategy in the infinitely repeated Bertrand game • Finitely repeated games • Optimal strategy: carrot and stick • Infinitely repeated Cournot game

15. Repeated games • Special case of dynamic games in which players face same “stage game” or constituent game in every period • overall payoff is a weighted sum or average of payoffs in each stage • past play cannot influence the actions available to players or their payoff functions (since the stage game is identical) • no investments / strategic commitments that alter the rules of the game, nor learning about the environment

16. Repeated games • But: history of the game does change (as we move through the game-tree), as can players’ one-shot actions • players’ strategies can be conditioned on the earlier actions taken by their opponents  new equilibria are possible • in games with imperfect info, the info structure may change over time as private information may be revealed by players’ actions

17. Repeated games (2) • Examples • Repeated prisoners’ dilemma (collusion game) • Sequential entry game (chain store paradox) • May be finitely or infinitely repeated • If game is finite (in no. of stages and actions), with perfect information, then it has at least one SPE in pure strategies • If the stage game has a unique NE, then the finitely repeated game has a unique SPE in which the NE is played in every round • If stage game has multiple NE, then the finitely repeated game has multiple SPE, and these may include outcomes that are not a NE of the stage game (especially in early rounds)

18. Infinitely repeated games • Problem • No “last round” so cannot use backward induction • Game is not finite, so existence and uniqueness of SPE cannot be guaranteed • “Folk theorem”: multiple equilibria and indeterminacy

19. Infinitely repeated Prisoners’ dilemma • Game is repeated an infinite number of times • Discount factor  < 1 (where  = ert) • Trigger strategy (or Nash reversion) • Collude in period 1, and for as long as both players keep on playing collude • Otherwise play defect • i.e., cooperate until someone deviates, but any deviation triggers permanent retaliation through reversion to the one-shot Nash equilibrium (assume this is Bertrand eqm) • Is this strategy an equilibrium?

20. Equilibrium in trigger strategies • Assume rival plays trigger; what will firm do? • Trigger: payoff = ½m (1++2+ … ) = ½m /(1–) • Defect: payoff = m (for one period only, after which 0) • Collusion is sustainable as long as ½m /(1–)  m • i.e.,   ½ ( = critical discount factor) • Thus, for sufficiently large , collusion is an eqm of the infinitely repeated game • Non uniqueness: other eqia also exist, including repeated play of the one-shot eqm {defect, defect} • Critical  is independent of collusive profit, m“Folk theorem”:collusion may occur at any price p  (c, pm]

21. Larger number of firms • What if n firms try to form a cartel? • Cartel payoff per firm = m /n • Assume defecting firm takes entire monopoly profit mfor one period • Non-coopve outcome is Bertrand ( = 0) • Solve for eqm in trigger strategies • Critical discount factor:   (n–1)/n • Higher  required as the number of firms n increases • Thus, collusion is harder to sustain for higher n

22. Why? Trigger: payoff = …= Defect: payoff = So maintain collusion if: )>1 or And since δ lies in range [0,1], as n increases, collusion harder to sustain.

23. How bad is this problem? Recall that the discount factor can be written in terms of a discount rate: But this means that increasing competitors from n=2 to n=3 cuts the interest rate threshold at which collusion pays by half…(r*(2) = 1; r*(3) = .5)

24. Finitely repeated Bertrand game • Recall game theory • If stage game has a unique NE: {defect, defect} • Then the unique SPE of the finitely repeated game is the NE outcome of the stage game in every period • Backward induction • Final stage: outcome of one-shot game is {defect, defect} • Penultimate stage: no reason to maintain cooperation since defection will occur in last round; game is equivalent to last stage  defect • Defect in every period, regardless of number of stages

25. Finite game with incomplete information • Backward induction result seems silly • Predicts a big difference between a game with 1 million rounds and one with an infinite number of rounds • Surely a game with very many rounds can sustain collusion, at least for a time? • E.g. Axelrod’s experiments with finitely repeated PD • Tend to see collusion early on in the game • Collusion breaks down towards the end • Way out of the paradox: incomplete information • Kreps, Milgrom, Roberts and Wilson (JET 1982)

26. KMRW (JET 1982) • Finite game with incomplete information (about type) • Player 1 believes player 2 may be a committed “trigger strategist” and assigns small probability  to this event • If 2 ever defects, this probability is updated to 0 • If remaining number of stages (s) is sufficiently large, collusion may be sustained • Check players’ incentives • For player 1 to play trigger rather than defect, given its beliefs about 2 • For player 2 to play trigger rather than defect, in order that 1’s beliefs about it are sustained

27. (Assume =1 for simplicity) • Player 1’s payoff (given belief , s remaining rounds) • Trigger: expected payoff ½m s + (1–)(–) • Defect: expected payoff m + (1–) 0 • Play trigger as long as • Similar analysis for player 2 • For any given , cooperation occurs early in the game, as long as it has a sufficiently long horizon • Fits Axelrod’s observations • Evolutionary approach: which rule survives when agents play pre-programmed strategies in a mixed population

28. “Stick and carrot” punishment • Alternative strategies to enforce collusion • Trigger strategy is “grim”: no forgiveness • Alternative: punish for a short time then revert to collusion • Abreu (JET 1986): optimal symmetric strategy involves • Stick: punishment period with high output ( ) and very low prices (worse than reversion to Nash eqm outcome); and • Carrot: return to collusion (q*) • Punishment must be credible • Firms must not renege on the punishment strategy, thus punishment cannot be too severe • If cheating occurs during punishment phase, punishment takes place for another period

29. Solving for “stick and carrot” equilibrium • B(q*) = BR when others play q* (i.e. payoff from cheating) • Payoffs (infinitely repeated game) • Collude: (q*) (1++2+3+ … ) • Defect: B(q*) + ( ) + (q*) (2+3+ … ) • Same after two periods; collude if (q*) (1+)  B(q*) + ( ) • I.e., collude if • Will firm cheat during punishment phase? • No cheating: ( ) + (q*) (+2+ … ) • Cheating: B( ) +  ( ) + (q*) (2+3+ … ) • Do not cheat if ( ) +  (q*)  B( ) +  ( )

30. Collusion with “stick and carrot” • Critical discount rate • Harsh punishment makes collusion easier to sustain • ( ) is a large negative number • Larger denominator  smaller critical discount factor  • E.g. large excess capacities make harsh punishment feasible  easier to sustain collusion • Better strategy than trigger: more severe and more credible punishment threat • But even greater multiplicity of equia

31. Puzzle: Infinitely repeated Cournot game • Calculate the critical discount factor  for eqm in trigger strategies in the infinitely repeated game • How does the sustainability of collusion depend upon • C ? • m ?

32. Trigger: Defect: So cooperate better than defect if:  so as the punishment payoff gets lower or payoff to cheating gets higher, it gets easier to collude; As punishment not so bad or payoff to cooperating not so good, harder to collude.

33. Extensions to the basic model • Detection (or reaction) lags • Stochastic demand: Rotemberg & Saloner (1986) • Imperfect monitoring: Green & Porter (1984) • Capacity constraints: Brock & Scheinkman (1985) • Asymmetric firms: Compte, Jenny & Rey (2002)

34. Detection lags • Suppose defection is not detected for 2 periods • punishment payoff = 0; cooperation payoff = ½ monopoly profit • Payoffs (duopoly) • Trigger: ½m / (1–) • Defect: m (1+) as receive monopoly  for 2 periods

35. Detection lags • Critical discount factor:   1/2  0.71 • i.e. collusion is harder to sustain (requires higher ) if price cutting is harder to detect (or to punish) • Thus, collusion becomes easier when • Firms can observe one another’s prices (or outputs), and • Firms can change output rapidly

36. Stochastic demand • Rotemberg & Saloner (AER 1986) • Each period, demand low (D1) or high (D2), prob ½:½ • Firms learn demand, then simultaneously choose prices • Incentive to cheat greatest when current D is high (D2) • Payoffs when current demand is D2 • Collude: uC = ½2m + ½ (½1m+ ½2m)  (1++2+ … ) = ½2m + ¼ (1m + 2m)  / (1–) • Defect: uD = 2m • Collusion requires  (½, 2/3) since 2m > 1m

37. Implications of stochastic demand • Stochastic demand makes collusion harder to sustain (in booms) • Price-cutting likeliest during booms • Could alter the collusive “agreement” by setting a price below the monopoly level during periods of high demand • Reduces incentive to cheat in these periods  Prices move counter-cyclically: R&S provide some evidence for this from the cement industry

38. Imperfect monitoring • Green and Porter (Ecta 1984) • Quantity-setting oligopoly • Market price depends on total output and demand: p(Qt, t) • Asymmetric information: firms do not observe rival q • D fluctuates randomly, also unobserved (t) [unlike R&S] • Thus, observation of a low price is a noisy signal • Could mean someone has defected, or that demand is low • Equilibrium strategy • Produce share of monopoly q*, until price falls below • Then produce > q* for T periods (punishment phase), before reverting to q*

39. Implications of imperfect monitoring • Fully collusive outcome cannot be sustained • Observe price wars in slumps, not booms • Opposite outcome to Rotemberg & Saloner • Price wars are necessary part of cartel discipline • Though no cheating occurs in eqm • Collusion is harder to sustain if demand is very uncertain • Trigger price is carefully calculated to overcome incentive to cheat while minimising unnecessary price wars • Greater uncertainty raises the cost from wasteful price wars • NB: punishment is costly to implement, as q while p • Free-rider problem if more than 2 firms

40. Capacity constraints • Brock and Scheinkman (REStud 1985): exogenous, symmetric capacity constraints • n firms • Each with fixed capacity k • Constant marginal cost c up to capacity k • Linear demand • Solve as Bertrand supergame • Look for SPE in trigger strategies, to sustain collusion at pm • Capacity constraint has 2 conflicting effects on collusion • Less incentive to cheat as cannot supply whole market • But ability to punish cheating is weaker

41. Brock & Scheinkman’s results • Standard result in n • Higher n raises critical  = (n–1)/n • Harder to sustain collusion as difference between share of cartel profit (m/n) and entire profit (m) is greater • B&S results • Higher n has a non-monotonic effect on critical  • Difference between m/n and m is greater • But capacity available to punish, nk, is also greater • Other results • Maximum sustainable cartel p is non-monotonic in n • Higher k has a non-monotonic effect on critical 

42. Implications of capacity constraints • For fixed n  3, critical  is a non-monotonic fn of k • (a) total capacity little more than monopoly output: weak cartel, need large  • (b) retaliation threat dominates gain from defection: strengthens cartel, lower  • (c) gain from undercutting outweighs retaliation: need larger  • (d) defector doesn’t use full capacity: further increase in k is irrelevant

43. Asymmetries between firms • Compte, Jenny & Rey (EER 2002): repeated Bertrand game with asymmetric capacity constraints • Sustainability of collusion depends on • Capacity of largest firm: determines incentive to cheat • Aggregate capacity of other firms: ability to punish • When aggr. capacity low, asymmetry hinders collusion • Largest firm has strong incentive to cheat • Rivals’ ability to punish is limited • When aggr. capacity large, asymmetry helps collusion • Punishment is effective and collusion can be sustained

44. Example: 2 competitors with market shares s<1/2 and (1-s)>1/2 Firm with share s: colludes if   Therefore, the threshold for collusion becomes larger as s shrinks (so that the smaller firm loses market share).

45. Factors conducive to collusion: Summary • Number of firms • Ability to reach agreement, incentive to cheat • More complex when combined with capacity constraints • Barriers to entry • Symmetric firms (costs, products) • Homogenous goods: Bertrand outcome very unattractive • Observable prices (or outputs) + ability to change output rapidly • Also stable demand / low uncertainty • Capacity constraints • Little incentive to cheat as cannot supply whole market demand • But ability to punish cheating is also weaker • Asymmetries may help or hinder collusion, depending on aggr. level

46. Facilitating practices -examples “We will match any price by our competition” (meet the competition ) Two firms, currently charging £10 and splitting monopoly profits (on demand normalised to one unit). Both institute a price pledge No Price Pledge: Price Pledge: Firm B Firm B £10 £9.99 £10 £9.99 £10 £5, £5 £0, £9.99 £10 £5, £5 £4.98, £4.98 Firm A Firm A £9.99 £9.99, £0 £4.98, £4.98 £9.99 £4.98, £4.98 £4.98, £4.98 (Prisoner’s Dilemma) (Collusive Equilibrium)

47. Facilitating practices -examples Notice: It is in the interests of customers to enforce the pledge hassle costs can negate the pledge. Suppose it costs 2p to enforce so if B drops price and customer wishes to stay with A, obtains £9.99+2p = £10.01 as transaction price. Hence, better to consume from B: No Price Pledge: Price Pledge: Firm B Firm B £10 £9.99 £10 £9.99 £10 £5, £5 £0, £9.99 £10 £5, £5 £0, £9.99 Firm A Firm A £9.99 £9.99, £0 £4.98, £4.98 £9.99 £9.99, £0 £4.98, £4.98 (Prisoner’s Dilemma) (Prisoner’s Dilemma)

48. Facilitating practices -examples Notice: if advertised prices are used, they can be inflated so as to void the pledge Both pledge to meet advertised price, and A raises advertised price to £11, with 200% rebate on any price difference. If B keeps price of £10, implies A’s net price is £9 for customers and B’s price pledge not triggered. A gets all customers…so we remain in price-cutting equilibrium.

49. Facilitating practices • Increase observability of prices: facilitate collusion through monitoring • Market transparency: public prices; basing point pricing • Information exchange, e.g. through trade associations • Meet competition (MC) clause: customers report on rivals’ pricing • Commitment devices – facilitate collusion through punishments • MC clause: commitment to match rivals’ price cuts • Most favoured nation (MFN) clause • Entitles customer to lowest price given to any customer • Reduces incentive for selective price cuts (cheating) • Price leadership: helps solve coordination problem

50. Summary Repeated interaction among the same players opens the door for dynamic strategies, different from repeated static outcome. Given that explicit collusion barred, tacit collusion that exploits these dynamic strategies is observed. The conditions under which tacit collusion is likely can be derived by comparing cheating and collusive payoffs under a wide set of conditions and assuming particular classes of strategies (such as trigger strategies). Facilitating practices – commitments that affect the payoff structure also can promote collusive outcomes as well as being privately beneficial to (myopic) customers.