Game Theory

A set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their own strategy while the other players keep theirs unchanged. It represents a stable state of mutual best responses.

A canonical two-player game illustrating why two rational individuals might not cooperate, even when cooperation would yield a better outcome for both. Each player has an incentive to defect regardless of the other's choice.

A strategy that yields a higher payoff for a player regardless of what strategies the other players choose. When a player has a dominant strategy, rational play dictates that they should always choose it.

A game in which one player's gain is exactly equal to the other player's loss, so the total payoff across all players always sums to zero. These are purely competitive situations with no opportunity for mutual benefit.

A strategy in which a player randomizes over two or more pure strategies according to specific probabilities, rather than choosing a single deterministic action. Mixed strategy equilibria exist even when no pure strategy equilibrium does.

A refinement of Nash Equilibrium for sequential games requiring that the strategy profile constitutes a Nash Equilibrium in every subgame of the original game. It eliminates non-credible threats.

Often called 'reverse game theory,' mechanism design involves designing game rules and incentive structures so that self-interested players, acting strategically, produce a desired outcome. It is used to design auctions, voting systems, and markets.

A game in which players have incomplete information about other players' characteristics (types), such as their payoffs, strategies, or beliefs. Players form probabilistic beliefs about unknown information and maximize expected utility.

An application of game theory to biology and social evolution where strategies are not chosen rationally but spread through a population based on reproductive fitness. Evolutionarily stable strategies resist invasion by alternative strategies.

Games played multiple times between the same players, where the history of past play can influence future strategies. The Folk Theorem states that in infinitely repeated games, virtually any outcome can be sustained as an equilibrium if players are sufficiently patient.