Nash Equilibria with Irradical Probabilities

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Edan Orzech, Martin C. Rinard

Published: 2025, Last Modified: 03 May 2026CoRR 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
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 $m$).