Best Response

Game Theory · Axiom Academy

Understanding how rational players choose strategies given their opponents' actions A best response for player i is the strategy (or set of strategies) that maximizes player i 's payoff, given the strategy choices of all other players. BR i (s -i ) = Best Response function for player i s -i = Strategy profile of all players except i S i = Set of all available strategies for player i u i (s i , s -i ) = Payoff to player i from strategy profile 2. Finding Best Responses in a Payoff Matrix The circle/underline method is a systematic way to identify best responses. For each player, we examine each possible strategy of their opponent and mark the player's best response to that strategy. The animation below demonstrates finding best responses in a classic 2×2 game: 3. Step-by-Step Best Response Identification Let's systematically identify all best responses for both players in a coordination game. For Player 1: Compare payoffs in each column For Player 2: Compare payoffs in each row Cells where both payoffs are marked indicate mutual best responses 4. Best Response Correspondence vs. Function A best response can be either a function (unique) or a correspondence (set-valued) depending on whether there's one or multiple optimal strategies. The animation illustrates both cases: 5. Connection to Nash Equilibrium

This is the written version of the interactive lesson above. See the full Game Theory course.