Deviation from an agreement to set high prices has - a short-term gain: increased profit today - a long-term loss: deviation by the others later on

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1 Dynaic oligopoly theory Collusion price coordination Illegal in ost countries - Explicit collusion not feasible - Legal exeptions Recent EU cases - Switchgears approx 750 ill Euros in fines (January 007) - Elevators approx 1 billion Euros (February 007) - Rubber additives approx 50 ill Euros (May 007). Tacit collusion Hard to detect not any cases. Repeated interaction Theory of repeated gaes Deviation fro an agreeent to set high prices has - a short-ter gain: increased profit today - a long-ter loss: deviation by the others later on Tacit collusion occurs when long-ter loss > short-ter gain Tore Nilssen Strategic Copetition Lecture Slide 1

2 Model Two firs, hoogeneous good, C(q) = cq Prices in period t: (p 1t, p t ) Profits in period t: π 1 (p 1t, p t ), π (p 1t, p t ) History at tie t: H t = (p 10, p 0,, p 1, t 1, p, t 1 ) A fir s strategy is a rule that assigns a price to every possible history. A subgae-perfect equilibriu is a pair of strategies that are in equilibriu after every possible history: Given one fir s strategy, for each possible history, the other fir s strategy axiizes the net present value of profits fro then on. T nuber of periods T finite: a unique equilibriu period T: p 1T = p T = c, irrespective of H T. period T 1: the sae and so on Tore Nilssen Strategic Copetition Lecture Slide

3 T infinite (or indefinite) At period τ, fir i axiizes t = τ δ t τ i π ( p ) p t t 1,, 1 δ = 1 + r The best response to (c, ) is (c, ). But do we have other equilibria? Can p > c be sustained in equilibriu? Trigger strategies: If a fir deviates in period t, then both firs set p = c fro period t + 1 until infinity. [Optial punishent schees? Abreu J Econ Th 1986] Monopoly price: p = arg ax (p c)d(p) Monopoly profit: π = (p c)d(p ) A trigger strategy for fir 1: Set p 10 = p in period 0 In the periods thereafter, p 1t (H t ) = p, if H t = (p, p,, p, p ) p 1t (H t ) = c, otherwise Tore Nilssen Strategic Copetition Lecture Slide 3

4 If a fir collaborates, it sets p = p and earns π / in every period. The optiu deviation: p ε, yielding π for one period. An equilibriu in trigger strategies exists if: π (1 + δ + δ + ) π δ 1 δ 1 The sae arguent applies to collusion on any price p (c, p ]. Infinitely any equilibria. The Folk Theore. π π 1 Tore Nilssen Strategic Copetition Lecture Slide 4

5 Collusion when deand varies Deand stochastic. Periodic deand is low: D 1 (p) with probability ½ high: D (p) with probability ½ D 1 (p) < D (p), p. The deand shocks are i.i.d. Each fir sets its price after having observed deand. What are the best collusive strategies for the two firs? Trigger strategies: A deviation is followed by p = c forever. What are the best collusive prices? One price in lowdeand periods and one in high-deand periods: p 1 and p. π s (p) total industry profit in state s when both firs set p. With prices p 1 and p in the two states, each fir s expected net present value is: ( ) ( ) ( ) t 1 D1 p1 1 D p = ( ) V = δ p + t 0 1 c p c = = 1 [D 1 (p 1 )(p 1 c) + D (p )(p c)] 4( 1 δ ) π p π ( 1 ) + ( ) 4( 1 δ ) 1 p Tore Nilssen Strategic Copetition Lecture Slide 5

6 The best possible collusive price in state s is: p s = arg ax (p c)d s (p), s = 1,. π s = (p s c)d s (p s ), s = 1,. If the firs can collude on these prices, then: 1 V π + = π 41 δ ( ) A deviation in state s receives a gain equal to: π s For (p 1, p ) to be equilibriu prices, we ust have: π s ½π s + δv π s δv The difficulty is state (high-deand), since π 1 < π. The equilibriu condition becoes: π1 + π π δ 41 ( δ ) δ δ 0 π1 3 + π π1 0 < π < 1 1 < δ 0 < 3 Tore Nilssen Strategic Copetition Lecture Slide 6

7 But what if δ [ 1, δ 0 )? Can we still find prices at which the firs can collude? The proble is again state. We need to set p so that π1 + π( p) π( p) δ 41 ( δ ) δ π ( p ) = π1 3δ 1 δ < 3 δ 3δ 1 π π 1 So: prices below onopoly price in high-deand state during boo. Could even be that p < p 1. But is this a price war? More realistic deand conditions: Autocorrelation business cycle. Collusion ost difficult to sustain just as the downturn starts. Haltiwanger & Harrington, RAND J Econ 1991 Kandori, Rev Econ Stud 1991 Bagwell & Staiger, RAND J Econ 1997 [Exercise 6.4] Tore Nilssen Strategic Copetition Lecture Slide 7

8 Epirical studies of collusion the railroad cartel - Porter Bell J Econ Ellison RAND J Econ 1994 collusion aong petrol stations - Slade Rev Econ Stud 199 collusion in the soft-drink arket: prices and advertising - Gasi, et al., J Econ & Manag Strat 199 collusion in procureent auctions - Porter & Zona J Pol Econ 1993 (road construction) - Pesendorfer Rev Econ Stud 000 (school ilk) Infrequent interaction Suppose the period length doubles. δ δ Collusion feasible if: δ 1 1 δ 0.71 Tore Nilssen Strategic Copetition Lecture Slide 8

9 Multiarket contact Market A: Frequent interaction, period length 1. Collusion if δ ½. Market B: Infrequent interaction, period length. Collusion if δ ½. (How could frequency vary across arkets?) What if both firs operate in both arkets? Can the firs obtain collusion in both arkets even in cases where δ < ½ < δ? A deviation is ost profitable when both arkets are open. Deviation yields: π Collusion yields: [π /] every period, plus [π /] every second period (starting today) Collusion can be sustained if: π [1 + δ + δ π + ] + [1 + δ + δ 4 + ] π δ 1 δ 4δ + δ δ Tore Nilssen Strategic Copetition Lecture Slide 9