{"ID":2894667,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09928","arxiv_id":"2507.09928","title":"Generalized Quantal Response Equilibrium: Existence and Efficient Learning","abstract":"We introduce a new solution concept for bounded rational agents in finite normal-form general-sum games called Generalized Quantal Response Equilibrium (GQRE) which generalizes Quantal Response Equilibrium~\\citep{mckelvey1995quantal}. In our setup, each player maximizes a smooth, regularized expected utility of the mixed profiles used, reflecting bounded rationality that subsumes stochastic choice. After establishing existence under mild conditions, we present computationally efficient no-regret independent learning via smoothened versions of the Frank-Wolfe algorithm. Our algorithm uses noisy but correlated gradient estimates generated via a simulation oracle that reports on repeated plays of the game. We analyze convergence properties of our algorithm under assumptions that ensure uniqueness of equilibrium, using a class of gap functions that generalize the Nash gap. We end by demonstrating the effectiveness of our method on a set of complex general-sum games such as high-rank two-player games, large action two-player games, and known examples of difficult multi-player games.","short_abstract":"We introduce a new solution concept for bounded rational agents in finite normal-form general-sum games called Generalized Quantal Response Equilibrium (GQRE) which generalizes Quantal Response Equilibrium~\\citep{mckelvey1995quantal}. In our setup, each player maximizes a smooth, regularized expected utility of the mix...","url_abs":"https://arxiv.org/abs/2507.09928","url_pdf":"https://arxiv.org/pdf/2507.09928v1","authors":"[\"Apurv Shukla\",\"Vijay Subramanian\",\"Andy Zhao\",\"Rahul Jain\"]","published":"2025-07-14T05:14:46Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.OC\"]","methods":"[]","has_code":false}