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.