Economics
Game Theory
Mathematical analysis of strategic interactions — when others' choices affect yours
Game theory is the mathematical study of strategic interactions where each player's outcome depends on others' choices. Founded by John von Neumann and Oskar Morgenstern (1944). Key concepts: players, strategies, payoffs, Nash equilibrium (no player wants to change strategy unilaterally). Applications: economics (oligopoly, auctions, bargaining), political science (voting, war), biology (evolution, animal behavior), computer science (algorithm design), business strategy. Famous examples: prisoner's dilemma, hawk-dove, ultimatum game. Nobel Prizes: Nash, Selten, Harsanyi (1994); Aumann, Schelling (2005); etc.
- FoundersJohn von Neumann, Oskar Morgenstern (1944)
- Key conceptNash equilibrium (Nash 1950)
- ComponentsPlayers, strategies, payoffs
- Famous examplePrisoner's dilemma
- Nobel PrizesMultiple (1994, 2005, 2007, 2014, etc.)
- ApplicationsEconomics, biology, political science, CS, philosophy
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Why game theory matters
- Economics. Strategic interactions.
- Business strategy. Competitor behavior.
- Political science. Voting, conflict.
- Auctions. Designing efficient mechanisms.
- Biology. Evolutionary stable strategies.
- Computer science. Algorithm design, AI.
- Philosophy. Ethics of cooperation.
Common misconceptions
- Just about games. Any strategic interaction.
- Solves all problems. Models simplify; not all real situations.
- Players always rational. Behavioral game theory adds psychology.
- One equilibrium. Multiple often exist.
- Easy to apply. Specifying games difficult.
- Solves cooperation. Shows difficulties; doesn't guarantee solutions.
Frequently asked questions
What's game theory?
Mathematical study of strategic interactions. Each player's outcome depends on what others do. Players: decision-makers. Strategies: possible actions. Payoffs: outcomes for each combination of strategies. Goal: find rational strategies. Tools: payoff matrices, decision trees, equilibrium analysis. Applies whenever strategic considerations matter.
What's the prisoner's dilemma?
Classic 2-person game. Two suspects arrested. If both stay silent: both get short sentences. If one talks (defects), other stays silent: defector free, silent one heavy sentence. If both talk: both medium sentences. Best outcome: both stay silent. But: each tempted to defect (gain benefit if other cooperates). Equilibrium: both defect (Pareto-dominated). Demonstrates: rational individual behavior leads to bad collective outcome.
What's Nash equilibrium?
Solution concept. Strategy combination where no player wants to unilaterally change. Each playing best response given others' strategies. Multiple equilibria possible. Famously: every game with finite strategies has Nash equilibrium (in mixed strategies). Reduces to: stable outcome no one wants to deviate from. John Nash Nobel Prize 1994 for this.
What's a dominant strategy?
Strategy best regardless of what others do. Strong concept. If player has dominant strategy: rational to play it. Prisoner's dilemma: defection is dominant for each. Even if other cooperates, defecting better; if defects, defecting better. Many games: no dominant strategy (best depends on others). Then: equilibrium analysis matters more.
What's cooperative vs non-cooperative game theory?
Different. Cooperative: players can make binding agreements. Coalition formation. Solutions: core, Shapley value, etc. Examples: bargaining, coalitions in politics. Non-cooperative: no binding agreements. Players act in own interest. Solutions: Nash equilibrium, evolutionary stable strategies. Different tools for different situations.
How is it applied in economics?
Many uses. (1) Oligopoly behavior: pricing, output decisions. (2) Auctions: optimal bidding. (3) Bargaining: wage negotiations. (4) Public goods: free-rider problem. (5) Market design: matching markets. (6) Mechanism design: designing rules to elicit desired behavior. (7) Information economics: signaling, screening. Major economic tool.
What about evolutionary game theory?
Game theory in biological context. Strategies passed on by reproduction (genes). Successful strategies multiply; unsuccessful disappear. Equilibrium: evolutionarily stable strategy (ESS). Examples: hawk-dove (aggression vs avoidance), kin selection. Maynard Smith (1982): foundational. Applications: animal behavior, human cooperation, language evolution. Different from rational-choice game theory.