{"ID":2895512,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09422","arxiv_id":"2507.09422","title":"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 $m$).","short_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 $m$).","url_abs":"https://arxiv.org/abs/2507.09422","url_pdf":"https://arxiv.org/pdf/2507.09422v1","authors":"[\"Edan Orzech\",\"Martin Rinard\"]","published":"2025-07-12T23:11:51Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.NT\"]","methods":"[]","has_code":false}