L21 Collusion

Page 1: Introduction

• Microeconomics

  • Course Code: ECA002

  • Topic: Collusion

    • Presented by: Luke Garrod

Page 2: Aims of the Lecture

• Objective:

  • Explore the concept of collusion in oligopolistic markets.

  • Understand differences between competitive outcomes and monopoly outcomes.

    • Monopoly results in worse outcomes than competitive models.

    • Competition generally reduces prices.

  • Analyze how firms may behave like monopolists in collusive scenarios.

  • Investigate the theory of repeated games to determine conditions for collusive behavior.

Page 3: Lecture Outline

1. The Prisoner's Dilemma and Oligopoly

2. Conditions Necessary for Oligopolists to Collude

3. Infinitely Repeated Prisoner's Dilemma

4. Finitely Repeated Prisoner's Dilemma

• Reading Material:

  • Core: Lipsey & Chrystal, Ch. 8

  • Extra: Perloff, Ch. 13.2 and 14.2

Page 4: The Prisoner's Dilemma

• Game Theory and Collusion:

  • Simplifying competition game model.

  • Scenario: Two criminals (A & B) & police interrogation.

• Strategies:

  • Confess (C) or Stay Silent (S).

• Payoff Outcomes:

  • (C, C): Both confess → 5 years each.

  • (C, S): A confesses → A goes free, B gets 10 years.

  • (S, C): A silent → A gets 10 years, B goes free.

  • (S, S): Both silent → 1 year each.

Page 5: Solution to the Prisoner's Dilemma

• Game Equilibrium:

  • Dominant strategy → (C, C) is Nash equilibrium.

  • Each player prefers to defect (confess) rather than cooperate, despite better outcomes when both cooperate.

  • Payoff Matrix:

    • Silent, Silent: -1, -1

    • Silent, Confess: 0, -10

    • Confess, Silent: -10, 0

    • Confess, Confess: -5, -5

Page 6: Best Response Functions

• Cournot and Bertrand Models

  • Cournot: Short-term incentives to deviate illustrated.

    • Firm A's output RA and Firm B's output RB.

  • Bertrand: Competing duopolies behaving like a Prisoner’s Dilemma.

Page 7: Conditions Necessary for Collusion

• Condition (1): Firms must interact repeatedly.

  • Incentives for deviation countered by credible long-term punishments (price wars).

• Condition (2): Firms must be aware of each other's strategies to punish deviations.

  • Forming cartels can help monitor adherence to agreements.

Page 8: Infinitely Repeated Prisoner's Dilemma

• Game Dynamics:

  • Repeated game setup leads to potential for collusion.

  • Strategies Outcomes:

  • Cooperation yields greater long-term payoffs vs. short-term gains from defection.

Page 9: Grim Trigger Strategies

• Strategy Definition:

  • Firms cooperate until one deviates, then revert to Nash equilibrium behavior indefinitely.

  • Assessing if this strategy is a Nash equilibrium.

Page 10: Calculating Short-Term Benefit

• Calculating the immediate benefit from deviation.

  • Payoffs:

    • Cooperate: 150

    • Deviate: 200

  • Short-term Benefit = 200 - 150 = 50.

Page 11: Calculating Present Value of Future Payoffs

• Importance of present value in economic decisions.

  • Implications of interest rates on future payouts.

Page 12: Future Value Calculations

• Deriving equivalences in terms of investment over time for two periods.

Page 13: Discounted Payoffs

• Expected payoffs in future periods discounted to present value.

  • Formula for expected present discounted value of continuous payoffs.

Page 14: Calculating Long-Term Punishment

• Evaluating long-term effects of deviation on conflicts in collusion scenarios.

  • Payoff differences for ongoing cooperative actions vs. defecting actions.

Page 15: Long-Term vs. Short-Term Benefits

• Nash Equilibrium Conditions:

  • Short-term benefits vs. long-term penalties,

  • Equilibrium exists if short-term benefits are outweighed by long-term consequences.

Page 16: Finitely Repeated Prisoner's Dilemma

• Is (cooperate, cooperate) a Nash equilibrium?

  • Use backward induction to explore Nash equilibrium in subgames.

  • Results suggest inevitable deviation in final periods.

Page 17: Summary of Conditions for Collusion

• Market Dynamics:

  • Price makers react strategically within oligopolistic structures.

  • Limited number of sellers with high barriers to entry can lead to monopolistic behavior.

Page 18: Post-Lecture Capabilities

1. State conditions for oligopoly collusion.

2. Represent oligopolies using Prisoner’s Dilemma.

3. Derive the critical discount factor for infinitely repeated prisoner's dilemma.

4. Describe finitely repeated dilemma equilibria.

Page 19: Proof for Discount Factor Convergence

• Mathematical proof showcasing convergence for future payout values.

Page 20: Private Study Exercises

• Game Verification:

  • Confirm characteristics of one-shot and repeated games.

  • Compute short-term benefits and long-term punishments in scenarios.