Thermal Min-Max Games: Unifying Bounded Rationality and Typical-Case Equilibrium
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917276522905600 |
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| author | Ichikawa, Yuma |
| author_facet | Ichikawa, Yuma |
| contents | Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and players exhibit bounded rationality. We introduce thermal min-max games, a thermodynamic relaxation that unifies bounded and perfect rationality by assigning each player a temperature to regulate their rationality level. To analyze typical behavior in the large-strategy limit, we develop a nested replica framework for this relaxation. This theory provides tractable predictions for typical equilibrium values and mixed-strategy statistics as functions of rationality strength, strategy-count aspect ratio, and payoff randomness. Numerical experiments demonstrate that these asymptotic predictions accurately align with the equilibrium of finite games of moderate size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermal Min-Max Games: Unifying Bounded Rationality and Typical-Case Equilibrium Ichikawa, Yuma Computer Science and Game Theory Disordered Systems and Neural Networks Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and players exhibit bounded rationality. We introduce thermal min-max games, a thermodynamic relaxation that unifies bounded and perfect rationality by assigning each player a temperature to regulate their rationality level. To analyze typical behavior in the large-strategy limit, we develop a nested replica framework for this relaxation. This theory provides tractable predictions for typical equilibrium values and mixed-strategy statistics as functions of rationality strength, strategy-count aspect ratio, and payoff randomness. Numerical experiments demonstrate that these asymptotic predictions accurately align with the equilibrium of finite games of moderate size. |
| title | Thermal Min-Max Games: Unifying Bounded Rationality and Typical-Case Equilibrium |
| topic | Computer Science and Game Theory Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2602.14858 |