  Using methods from the statistical mechanics of disordered systems we analyze
the properties of bimatrix games with random payoffs in the limit where the
number of pure strategies of each player tends to infinity. We analytically
calculate quantities such as the number of equilibrium points, the expected
payoff, and the fraction of strategies played with non-zero probability as a
function of the correlation between the payoff matrices of both players and
compare the results with numerical simulations.
