We use techniques from the statistical mechanics of disordered systems to
analyse the properties of Nash equilibria of bimatrix games with large random
payoff matrices. By means of an annealed bound, we calculate their number and
analyse the properties of typical Nash equilibria, which are exponentially
dominant in number. We find that a randomly chosen equilibrium realizes 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 complemented by the
calculation of the properties of Nash equilibria in pure strategies.Comment: 6 pages, was "Self averaging of Nash equilibria in two player games",
main section rewritten, some new results, for additional information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm