International Journal of Game Theory
We consider zero-sum games (A, − A) and coordination games (A,A), where A is an m-by-n matrix with entries chosen independently with respect to the Cauchy distribution. In each case, we give an exact formula for the expected number of Nash equilibria with a given support size and payoffs in a given range, and also asymptotic simplications for matrices of a fixed shape and increasing size. We carefully compare our results with recent results of McLennan and Berg on Gaussian random bimatrix games (A,B), and describe how the three situations together shed light on random bimatrix games in general.
© Springer-Verlag 2006
David P. Roberts. Nash Equilibria in Cauchy-Random Zero-Sum and Coordination Matrix Games. International Journal of Game Theory 34 (2006), no. 2, 167-184.