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arXiv · 2605.27257

Nash Equilibria with Derangement Degree Probabilities

Edan Orzech·Martin Rinard
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Abstract

We prove for every $n\ge4$ the existence of an $n$-player game in normal form with integer payoffs that has a unique Nash equilibrium, which is fully mixed. In the equilibrium, each probability weight is an algebraic number of degree $\mathbin{!n}$ (the derangement number), and its minimal polynomial has Galois group $S_{\mathbin{!n}}$ and $\mathbin{!n}+1$ nonzero coefficients.

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Edan Orzech, Martin Rinard. 2026-05-26. Nash Equilibria with Derangement Degree Probabilities. https://arxiv.org/abs/2605.27257

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