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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09928 |
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| _version_ | 1866911054041186304 |
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| author | Shukla, Apurv Subramanian, Vijay Zhao, Andy Jain, Rahul |
| author_facet | Shukla, Apurv Subramanian, Vijay Zhao, Andy Jain, Rahul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Quantal Response Equilibrium: Existence and Efficient Learning Shukla, Apurv Subramanian, Vijay Zhao, Andy Jain, Rahul Computer Science and Game Theory Optimization and Control 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. |
| title | Generalized Quantal Response Equilibrium: Existence and Efficient Learning |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2507.09928 |