Normal-form game

A game represented by its players, available strategies, and each player's payoff for every combination of strategies. It makes strategic interdependence explicit in a payoff table or equivalent mathematical structure.

Player (game theory): An agent whose choice can affect outcomes in a game. Each player chooses a strategy and receives a payoff based on the full strategy profile.
Best response: A strategy that gives a player the highest payoff given the other players' strategies. It identifies each player's optimal choice at a specified strategy profile.
Prisoner's dilemma: A two-player game in which individually rational choices produce a worse outcome for both than mutual cooperation. Its payoff matrix isolates the conflict between private incentives and collective benefit.
Extensive-form game: A game representation that specifies decision order, available actions, and information at each decision point. It retains sequential structure that a normal-form payoff table may obscure.
Nash's theorem: The theorem that every finite game has a Nash equilibrium when players may use mixed strategies. It guarantees an equilibrium for every finite normal-form game under standard assumptions.
Strategy (game theory): A complete plan of action available to a player in a game. Strategies define the choices whose combinations determine the game's payoffs.
Nash equilibrium: A strategy profile in which no player can gain by changing strategy alone. It is the central stability condition applied to normal-form games.
Battle of the sexes (game theory): A coordination game in which two players prefer being together but favor different outcomes. Its payoffs model coordination when players agree on meeting but disagree on what to choose.
Imperfect-information game: A game in which at least one player lacks knowledge of some earlier actions or relevant state. Normal-form representation can encode strategic uncertainty without displaying its information structure.
Minimax theorem: A theorem stating that in finite two-player zero-sum games, each player has a strategy guaranteeing a value equal to the opponent's minimax value. It gives a precise solution for the zero-sum games represented in normal form.

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