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 - Gas approx. 1.1 billion Euros in fines (009) - Car glass approx. 1.4 billion Euros (008) - Elevators approx. 800 illion Euros (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: 1 (p 1t, p t ), (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, fir i axiizes t i p1 t, pt, 1 1 r t 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? Renegotiation-proofness?] Monopoly price: p = arg ax (p c)d(p) Monopoly profit: = (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 / in every period. The optiu deviation: p, yielding for one period. An equilibriu in trigger strategies exists if: ( ) The sae arguent applies to collusion on any price p (c, p ]. Infinitely any equilibria. The Folk Theore. 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. 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 p t 0 1 c p c 1 = [D 1 (p 1 )(p 1 c) + D (p )(p c)] 41 1p1 p = 4 1 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,. s = (p s c)d s (p s ), s = 1,. If the firs can collude on these prices, then: 1 V 41 A deviation in state s receives a gain equal to: s For (p 1, p ) to be equilibriu prices, we ust have: s ½ s + V s V The difficulty is state (high-deand), since 1 <. The equilibriu condition becoes: < < 1 1 < 0 < 3 Tore Nilssen Strategic Copetition Lecture Slide 6
7 But what if [ 1, 0 )? Can we still find prices at which the firs can collude? The proble is again state. We need to set p so that 1 p p 41 p < 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. Collusion feasible if: Tore Nilssen Strategic Copetition Lecture Slide 8
9 Multiarket contact Market A: Frequent interaction, period length 1. Collusion if ½. Market B: Infrequent interaction, period length. Collusion if 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 < ½ <? A deviation is ost profitable when both arkets are open. Deviation yields: Collusion yields: [ /] every period, plus [ /] every second period (starting today) Collusion can be sustained if: [ ] + [ ] Tore Nilssen Strategic Copetition Lecture Slide 9
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