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Econ 200: Strategic Interactions

Pareto Criterion

  • Definition: Allocation A is preferable to allocation B if at least one party is strictly better off with A and no party is worse off.
  • Terminology:
    • A Pareto dominates B
    • A is a Pareto improvement over B
  • Efficient Allocations: An allocation is Pareto efficient if it is not dominated by any other allocation.

Social Preferences

  • Concept: Individuals may consider the welfare of others in their decisions, leading to possible resolutions of social dilemmas.
  • Types of Social Preferences:
    • Altruism: Willingness to incur a cost for the benefit of others.
    • Reciprocity: Responding to others' actions with similar actions (both good and bad).
    • Inequality Aversion: Preference for more equal distributions of resources.
    • Spite: Preferencing outcomes that harm others, even at a personal cost.

Public Goods Game

  • Definition of Public Goods:
    • Non-excludable: Cannot prevent individuals from using the good.
    • Non-rival: One person's use does not diminish the good for others.
    • Example: If four farmers consider contributing to an irrigation project:
    • Private cost = $10
    • Individual benefit = $8
    • Social benefit = 4*$8 = $32
    • Dominant Strategy: No one contributes, leading to a Nash equilibrium of $0 for everyone.
  • Similarities to Prisoners’ Dilemma: Participants face individual versus collective interests.

Repeated Games

  • Concept: In ongoing interactions, players may choose to cooperate to foster future cooperation.
  • Strategy: Tit-for-tat - mimic the opponent’s last action to encourage cooperation.

Economic experiments

  • Role: Economists use lab experiments for testing theories, as whole economies cannot be manipulated ethically.
  • Peer Punishment: Players can penalize low contributors to enhance group contributions.

Ultimatum Game

  • Structure: Two players split $100:
    • Proposer offers an amount to the responder.
    • Responder can accept or reject (if rejected, both get $0).
  • Nash Equilibrium: Typically, offers below $20 are rejected due to fairness concerns.
  • Cultural Differences: Varying responses observed across cultures (e.g., Kenyan farmers offer more than U.S. students).

Multiple Equilibria

  • Concepts: Situations where there are multiple strategies that can provide the same outcome, requiring consensus.
  • Example: Driving conventions in different countries - both left and right driving can be equilibria.

Assurance Games

  • Definition: Situations where cooperation is beneficial but depends on mutual trust.
  • Examples:
    • Social norms vs. law-breaking behavior.
    • Choosing programming languages (Java vs. C++).

Summary of Social Interactions

  • Game Theory Application: Used to model social interactions and conflicts of interest.
  • Key Outcomes:
    • Mutual benefits from self-interest (Invisible Hand Game).
    • Potential losses from conflicts (Prisoners’ Dilemma).
    • Cooperation can arise from altruism, repetition, or institutions that enforce positive behavior.