Mixed Equilibrium Examples

Game Theory · Axiom Academy

EXAMPLE Mixed Equilibrium Examples Unit 2 - Dominance and Nash Equilibrium: Computing mixed strategy equilibria step-by-step Excellent work! You've mastered mixed strategy Nash equilibrium calculations. Here's what we learned: Indifference Principle: In a mixed strategy Nash equilibrium, each player must be indifferent between the pure strategies they are mixing over. This means the expected payoffs from each pure strategy must be equal. Opponent Makes You Indifferent: Player 1's mixing probabilities are determined by making Player 2 indifferent, and vice versa. This is a crucial insight for solving mixed equilibria. Expected Payoff Calculation: At a mixed Nash equilibrium, calculate expected payoffs by multiplying probabilities with corresponding payoffs and summing across all strategy profiles. Existence of Pure vs. Mixed: Games like Matching Pennies have no pure strategy Nash equilibrium but always have at least one mixed strategy Nash equilibrium (by Nash's theorem). These techniques apply to any 2x2 game. Practice identifying when to look for mixed equilibria and how to set up the indifference equations systematically!

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