Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909049815040000 |
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| author | Gordji, Madjid Eshaghi Abounoori, Esmaiel Berahman, Mohamadali |
| author_facet | Gordji, Madjid Eshaghi Abounoori, Esmaiel Berahman, Mohamadali |
| contents | We extend the concept of meta-Nash equilibrium, introduced by Eshaghi Gordji and Bagha [2026] for complete-information games, to environments with incomplete information. We define a meta-Bayesian Nash equilibrium as a profile of type-dependent mixed meta-strategies together with an environmental move such that no player type can profitably deviate and the environment cannot improve its expected payoff. For each transformed game, meta-payoffs are determined by the unique Bayesian Nash equilibrium of that game. Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium. Several illustrative examples, including adaptive subsidy competition, cybersecurity protocol selection, and platform rule formation, demonstrate that private information at the meta-level plays an essential role in endogenous game transformation. The framework contains both classical Bayesian games and complete-information meta-games as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem Gordji, Madjid Eshaghi Abounoori, Esmaiel Berahman, Mohamadali Theoretical Economics General Economics Economics We extend the concept of meta-Nash equilibrium, introduced by Eshaghi Gordji and Bagha [2026] for complete-information games, to environments with incomplete information. We define a meta-Bayesian Nash equilibrium as a profile of type-dependent mixed meta-strategies together with an environmental move such that no player type can profitably deviate and the environment cannot improve its expected payoff. For each transformed game, meta-payoffs are determined by the unique Bayesian Nash equilibrium of that game. Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium. Several illustrative examples, including adaptive subsidy competition, cybersecurity protocol selection, and platform rule formation, demonstrate that private information at the meta-level plays an essential role in endogenous game transformation. The framework contains both classical Bayesian games and complete-information meta-games as special cases. |
| title | Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem |
| topic | Theoretical Economics General Economics Economics |
| url | https://arxiv.org/abs/2605.16926 |