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Industrial Organization I

Industrial Organization I. Market Power O ligopoly models: Dynamic games and collusion. Collusion. Very important topic: Theory How can it be achieved? What factors affect collusion? Focus on implicit collusion Empirics/antitrust: How can it be detected?

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Industrial Organization I

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  1. Industrial Organization I Market Power Oligopoly models: Dynamic games and collusion

  2. Collusion • Very important topic: • Theory • How can it be achieved? • What factors affect collusion? • Focus on implicit collusion • Empirics/antitrust: • How can it be detected? • What factors contribute to collusion? • What are the damages to society (consumer)? • Focus on explicit collusion

  3. Collusion • Very important topic: • Theory • How can it be achieved? • What factors affect collusion? • Focus on implicit collusion • Empirics/antitrust: • How can it be detected? • What factors contribute to collusion? • What are the damages to society (consumer)? • Focus on explicit collusion

  4. Collusion and Repeated Games • Collusion is not an equilibrium of a one-shot game • However, collusion is observed in many markets • Types of collusion: • Explicit: direct price agreement (OPEC) - illegal • Tacit: no communication, but data looks like it • How to explain tacit collusion as an equilibrium? • One way: Relax assumption of 1-time interaction

  5. Collusion and Repeated Games • 1-shot game: There is no incentive to charge collusive price • With repetitive interaction (t=1,…..): • Is it possible an equilibrium , (t=1,…..)?

  6. Collusion and Repeated Games • What is different with repetitive interaction? • Punishment • Reputation • Intuition: • Period 1: P1=P2=PM • Period 2: There is some “confidence” and it might be easier to collude again • Explicit collusion is illegal • But, tacit collusion is theoretically possible (?)

  7. Theory of Dynamic Games • “Repeated interaction”, also “Supergames” • Assume: (Betrand environment) • 2 firms • Homogeneous products • C1=C2=C (constant marginal cost). • Firms face each other T+1 times • Lower price firm gets whole market • If p1=p2, both firms share half the market

  8. Theory of Dynamic Games • Denote firm i’s profit at time t, t=(0,…,T): • Each firm maximizes present value of profits:

  9. Theory of Dynamic Games • close to 1 means patient firms (i.e. weigh future profits heavily, low i) • close to 0 means impatient firms (i.e. no weight on future profits, high i) • Suppose T (# of times played) is finite • How is the equilibrium solved? • Backwards induction: solve equilibrium in last period and work backwards. • Is this different from the Betrand paradox?

  10. Theory of Dynamic Games • Last period is a static one-shot game (history does not matter): p1T=p2T=c • What is equilibrium at T-1? Since at T history is not relevant, T-1 is as if it was the last period: p1T-1=p2T-1=c • So on… • If T is finite, dynamics contribute nothing…(in theory)

  11. Theory of Dynamic Games • What if T=infinity? • Equilibrium: set of strategy profiles or histories P*1=(p*10, p*11,…, p*1T) and P*2 =(p*20,…, p*2T) such that no deviation can yield higher PV payoffs:

  12. Trigger strategies • The interesting question is whether pm can be sustained in the equilibrium path • Let’s suppose players use a “trigger strategy”: revert to Bertrand (forever) if someone deviates • Then, for pit=pm to be and equilibrium, it must be the case that:

  13. Example: Prisoner’s Dilemma Firm 2 Firm 1

  14. Trigger Strategies: Example • Firms discount future earnings at rate “i” • Each firm faces “trade-off” in each period t: • Deviate and face competition forever, or • Cooperation forever Present value of deviating today Present value of always cooperating

  15. Trigger Strategies: Example • PV of deviation: • PV of cooperation: • If firms stick to these trigger strategies, collusion can be an equilibrium if C≥D: a

  16. Trigger Strategies: Example • Large delta (small i) denotes a patient firm: • Future earnings are relatively important • Therefore, infinite punishment is more severe • Collusive equilibrium condition: • Firms must be sufficiently patient • Intuition: for impatient firms (low delta, high i), future punishment of P=MC forever is not very important

  17. Trigger strategy equilibrium: Key Points • It is important to identify the deviator • Punishment is for everyone • Collusion can be an equilibrium even with non-cooperative game theory • Important: • Any price between c and pm can be sustained with trigger strategies as long as delta>delta* (“folk theorem”) • Too many things are theoretically possible.

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