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

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

1999-05-06

arxiv.org/abs/cond-mat/9905076v2

Europhys. Lett.,48 (2), 129-135 (1999)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, was "Self averaging of Nash equilibria in two player games", main section rewritten, some new results, for additional

Scientific paper

10.1209/epl/i1999-00456-2

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.

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