What Is a Game?
In game theory, a 'game' has players (decision-makers), strategies (possible actions), and payoffs (outcomes for each combination of strategies). Games can be zero-sum (one player's gain is another's loss — poker, chess) or non-zero-sum (both can gain or lose — trade negotiations, climate agreements).
The Prisoner's Dilemma
The prisoner's dilemma is game theory's most famous example. Two suspects are interrogated separately. If both stay silent, each gets 1 year. If one betrays and the other stays silent, the betrayer goes free and the silent one gets 3 years. If both betray, both get 2 years. Rational self-interest leads both to betray — producing the worst collective outcome. The dilemma models arms races, environmental agreements, and corporate competition.
Nash Equilibrium
John Nash (1950) defined an equilibrium concept: a set of strategies where no player can benefit by changing strategy unilaterally, given what others are doing. Every finite game has at least one Nash equilibrium (possibly in mixed strategies). Nash equilibrium predicts stable outcomes in strategic interactions — though not always the best ones for participants collectively.
Evolutionary Game Theory
Biologists (Maynard Smith, Price) applied game theory to evolution: strategies that produce higher fitness spread in populations. The hawk-dove game models conflict over resources; evolutionarily stable strategies are the biological equivalent of Nash equilibria. This framework explains the evolution of altruism, aggression, and cooperation without assuming rational deliberation.
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What is Nash equilibrium?
A Nash equilibrium is a set of strategies in a game where no player can improve their outcome by changing their strategy alone, given what other players are doing. It predicts stable outcomes in strategic interactions. Named for mathematician John Nash, who proved every finite game has at least one such equilibrium.
What is the prisoner's dilemma?
The prisoner's dilemma is a game where two rational players, unable to communicate, each choose to betray the other rather than cooperate — producing a worse outcome for both than if they had cooperated. It models situations where individual rationality leads to collective irrationality, including arms races, environmental agreements, and price competition.
Who invented game theory?
Game theory was founded by mathematician John von Neumann and economist Oskar Morgenstern in their 1944 book Theory of Games and Economic Behavior. John Nash extended it in 1950 with his equilibrium concept, earning the 1994 Nobel Memorial Prize in Economics.