Statistical mechanics of random two-player games

TL;DR

This paper applies statistical mechanics techniques to analyze large random bimatrix games, deriving analytical expressions for equilibria and payoffs, and validating results with simulations.

Contribution

It introduces a novel application of statistical mechanics to characterize the properties of large random bimatrix games, including equilibrium count and strategy distribution.

Findings

Number of equilibrium points as a function of payoff correlation

Expected payoff varies with payoff matrix correlation

Fraction of strategies played with non-zero probability depends on matrix correlation

Abstract

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.