A NOTE ON THE PROBABILITY OF K-PURE NASH EQUILIBRIA IN MATRIX GAMES

A formula is derived for the probability that a ''randomly selected'' n-person matrix game has exactly k pure strategy equilibria. It is shown that for all n greater than or equal to 2, this probability converges to e(-1)/k! as the sizes of the strategy sets of at least two players increase without bound. Thus the number of pure strategy equilibria in large random n-person matrix games is approximately Poisson distributed with mean one. The latter is a known result obtained by a new proof in this note. Journal of Economic Literature Classification Number: C72. (C) 1995 Academic Press, Inc.