On Random Symmetric Bimatrix Games

Abstract

An experiment was conducted on a sample of [Formula: see text] randomly generated symmetric bimatrix games with size [Formula: see text] and [Formula: see text]. Distribution of support sizes and Nash equilibria are used to formulate a conjecture: for finding a symmetric NEP it is enough to check supports up to size [Formula: see text] whereas for nonsymmetric and all NEPs this number is [Formula: see text] and [Formula: see text], respectively. If true, this enables us to use a Las Vegas algorithm that finds a Nash equilibrium in polynomial time with high probability.