Game Theory Course: 3.2 Computing Mixed-Strategy Nash Equilibria of 2 x 2 Strategic-Form Games

Jim Ratliff

Game Theory

Nash Equilibrium

Article

We'll now see explicitly how to find the set of (mixed-strategy) Nash equilibria for general two-player games where each player has a strategy space containing two actions (i.e. a "2x2 matrix game"). We first compute the best-response correspondence for a player. We partition the possibilites into three cases: The player is completely indifferent; she has a dominant strategy; or, most interestingly, she plays strategically (i.e., based upon her beliefs about her opponent's play).