Dominance and Nash Summary

Game Theory · Axiom Academy

SUMMARY Dominance and Nash Equilibrium Unit 2: Key concepts for analyzing strategic interactions and predicting outcomes Strictly Dominant Strategy: A strategy that yields strictly higher payoff than any other strategy, regardless of what opponents do Weakly Dominant Strategy: A strategy that yields at least as high a payoff as any other strategy, and strictly higher for at least one opponent action Dominated Strategy: A strategy that is always inferior to another strategy; rational players never play dominated strategies Dominance Solvability: A game is dominance solvable if iterated elimination yields a unique outcome Best Response Function: For each action of opponents, identifies the strategy (or strategies) that maximizes a player's payoff Notation: BR i (s -i ) is the set of player i 's best responses to opponents' strategies s -i Key Property: A strategy is never a best response if and only if it is strictly dominated Multiple Best Responses: A player may have several equally good best responses to the same opponent action Mutual Best Responses: Each player is playing a best response to what others are doing No Profitable Deviations: No player has incentive to change strategy given opponents' strategies Self-Enforcing: If all players expect others to play the equilibrium, each player's optimal choice is to play their equilibrium strategy

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