Entropy and typical properties of Nash equilibria in two-player games

We use techniques from the statistical mechanics of disordered systems to a nalyse the properties of Nash equilibria of bimatrix games with large rando m payoff matrices. By means of an annealed bound, we calculate their number and analyse the properties of typical Nash equilibria, which are exponenti ally dominant in number. We find that a randomly chosen equilibrium realize s almost always equal payoffs to either player. This value and the fraction of strategies played at an equilibrium point are calculated as a function of the correlation between the two payoff matrices. The picture is compleme nted by the calculation of the properties of Nash equilibria in pure strate gies.