Best response

A strategy that maximizes a player's payoff given the strategies chosen by other players. It can be a single strategy or a set of tied strategies.

Game theory: The mathematical study of strategic interaction among decision-makers. Best responses are defined within games of strategic interaction.
Best-response function: A rule assigning each opponents’ strategy profile the strategies that maximize a player's payoff. It formalizes how a player's optimal choice changes with others’ choices.
Bertrand competition: A model in which firms compete by setting prices for products consumers regard as identical. A firm’s best price depends on rivals’ prices and the rules of the market.
Strictly dominant strategy: A strategy that gives a player a strictly higher payoff than every alternative against every opponents’ strategy profile. It is best against all choices, while a best response need only fit one profile.
Strategy (game theory): A complete plan specifying a player's action in every situation the game allows. A best response is a strategy selected from a player's available plans.
Best-response correspondence: A set-valued mapping from opponents’ strategies to all payoff-maximizing strategies. Tied optimal strategies require a correspondence rather than a single-valued function.
First-price sealed-bid auction: An auction in which the highest bidder wins and pays their own submitted bid. Bidders choose best-response bids by balancing winning probability against payment.
Maximin strategy: A strategy that maximizes a player's worst possible payoff across opponents’ choices. Maximin choice protects against the worst case rather than maximizing payoff at a specified profile.
Payoff: A numerical representation of the outcome a player receives in a game. Comparing payoffs determines which strategy is a best response.
Iterated elimination of strictly dominated strategies: A procedure that repeatedly removes strategies that always yield lower payoffs than some alternative. Removing such strategies can simplify the search for mutual best responses.

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