Existence and Uniqueness Theorem of Continuous and Monotone Bayesian Nash Equilibrium and Stability Analysis
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909013901312000 |
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| author | Su, Ziheng Xu, Huifu |
| author_facet | Su, Ziheng Xu, Huifu |
| contents | Since the seminal work by Meirowitz, there has been growing attention on the existence and uniqueness of continuous Bayesian Nash equilibria. In the existing literature, existence is typically established using Schauder's fixed-point theorem, relying on the equicontinuity of players' best response functions. Uniqueness, on the other hand, is usually derived under additional monotonicity conditions. In this paper, we revisit the issues of existence and uniqueness, and advance the literature by establishing both simultaneously using the Banach fixed-point theorem under a set of moderate conditions. Furthermore, we analyze the stability of such equilibria with respect to perturbations in the joint probability distribution of type parameters, offering theoretical support for the application of Bayesian Nash equilibrium models in data-driven contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness Theorem of Continuous and Monotone Bayesian Nash Equilibrium and Stability Analysis Su, Ziheng Xu, Huifu Optimization and Control 47H09, 90C31, 91A06, 91A10, 91A27 Since the seminal work by Meirowitz, there has been growing attention on the existence and uniqueness of continuous Bayesian Nash equilibria. In the existing literature, existence is typically established using Schauder's fixed-point theorem, relying on the equicontinuity of players' best response functions. Uniqueness, on the other hand, is usually derived under additional monotonicity conditions. In this paper, we revisit the issues of existence and uniqueness, and advance the literature by establishing both simultaneously using the Banach fixed-point theorem under a set of moderate conditions. Furthermore, we analyze the stability of such equilibria with respect to perturbations in the joint probability distribution of type parameters, offering theoretical support for the application of Bayesian Nash equilibrium models in data-driven contexts. |
| title | Existence and Uniqueness Theorem of Continuous and Monotone Bayesian Nash Equilibrium and Stability Analysis |
| topic | Optimization and Control 47H09, 90C31, 91A06, 91A10, 91A27 |
| url | https://arxiv.org/abs/2511.15457 |