Nash Equilibria with Irradical Probabilities

Abstract

We present for every $n\ge4$ an $n$-player game in normal form with payoffs in $\{0,1,2\}$ that has a unique, fully mixed, Nash equilibrium in which all the probability weights are irradical (i.e., algebraic but not closed form expressible even with $m$-th roots for any integer $m$).