Finding Nash Equilibria

Game Theory · Axiom Academy

LESSON Finding Nash Equilibria Unit 2 - Dominance and Nash Equilibrium 1. The Underline Method: Finding Best Responses The first step in finding Nash Equilibria is to identify each player's best response to each strategy of their opponent. A best response is the strategy that maximizes a player's payoff given what the other player is doing. We mark best responses by underlining the payoffs in the game matrix: Row player's best responses: For each column, find the highest payoff for the row player and underline it Column player's best responses: For each row, find the highest payoff for the column player and underline it 2. Step-by-Step: Analyzing a Coordination Game Let's apply the underline method to a classic coordination game. Watch as we systematically identify each player's best responses. 3. Finding Nash Equilibria: Mutual Best Responses A Nash Equilibrium occurs when both players are playing best responses simultaneously . In the matrix, this appears as a cell where both payoffs are underlined . After underlining all best responses, simply circle the cells where both payoffs are underlined. These are your Nash Equilibria! 4. Example: Battle of the Sexes Let's practice with another game. In the "Battle of the Sexes," two players want to coordinate their activities but have different preferences. Watch as we identify the Nash Equilibria. 5. What If There's No Pure Strategy NE?

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