Nash Equilibrium and Belief Evolution in Differential Games
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916949934473216 |
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| author | Zhou, Jiangjing Petrosian, Ovanes Zhang, Ye Gao, Hongwei |
| author_facet | Zhou, Jiangjing Petrosian, Ovanes Zhang, Ye Gao, Hongwei |
| contents | This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical proofs leveraging key probability theorems demonstrate that players' beliefs converge to the true parameter values, ensuring stability and accuracy in long-term estimations. We further derive Nash Equilibrium strategies with continuous Bayesian updating for players, emphasizing the role of belief updates in decision-making processes. Additionally, we establish the convergence of Nash Equilibrium strategies with continuous Bayesian updating. The efficacy of both continuous and dynamic Bayesian updating is examined in the context of pollution control games, showing convergence in players' estimates under small time intervals in discrete scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nash Equilibrium and Belief Evolution in Differential Games Zhou, Jiangjing Petrosian, Ovanes Zhang, Ye Gao, Hongwei Multiagent Systems Computer Science and Game Theory This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical proofs leveraging key probability theorems demonstrate that players' beliefs converge to the true parameter values, ensuring stability and accuracy in long-term estimations. We further derive Nash Equilibrium strategies with continuous Bayesian updating for players, emphasizing the role of belief updates in decision-making processes. Additionally, we establish the convergence of Nash Equilibrium strategies with continuous Bayesian updating. The efficacy of both continuous and dynamic Bayesian updating is examined in the context of pollution control games, showing convergence in players' estimates under small time intervals in discrete scenarios. |
| title | Nash Equilibrium and Belief Evolution in Differential Games |
| topic | Multiagent Systems Computer Science and Game Theory |
| url | https://arxiv.org/abs/2509.11739 |