Nash Equilibrium

Game Theory · Axiom Academy

Unit 2: Dominance and Nash Equilibrium Formally, for each player i , the equilibrium strategy s* i must maximize player i 's payoff, given the strategies of all other players s* -i . Nash equilibrium requires that each player is playing a best response to what others are doing. This creates a state of mutual consistency. If player 1 is playing their best response to player 2's strategy, AND player 2 is playing their best response to player 1's strategy, then neither player wants to deviate. 3. No Unilateral Deviation Incentive At a Nash equilibrium, no player can improve their payoff by changing only their own strategy. The key word is "unilateral" - a single player acting alone. This doesn't mean players couldn't be better off if everyone changed strategies together, but no individual player has a reason to deviate on their own. 4. Nash Equilibrium as Stable Prediction Nash equilibrium is considered a stable prediction because once players reach it, they have no reason to move away from it. It represents a self-enforcing agreement : if all players believe others will play their equilibrium strategies, then each player's best response is to play their own equilibrium strategy.

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