Statistical mechanics of random two-player games

Using methods from the statistical mechanics of disordered systems, we anal yze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analyti cally calculate quantities such as the number of equilibrium points, the ex pected payoff, and the fraction of strategies played with nonzero probabili ty as a function of the correlation between the payoff matrices of both pla yers, and compare the results with numerical simulations.