Non-exchangeable evolutionary and mean field games and their applications
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| Format: | Preprint |
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2025
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| _version_ | 1866918212159930368 |
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| author | Yoshioka, H. Tsujimura, M. Tanaka, T. |
| author_facet | Yoshioka, H. Tsujimura, M. Tanaka, T. |
| contents | A replicator dynamic for non-exchangeable agents in a continuous action space is formulated and its well-posedness is proven in a space of probability measures. The non-exchangeability allows for the analysis of evolutionary games involving agents with distinct (and possibly infinitely many) types. We also explicitly connect this replicator dynamic to a stationary mean field game, which determines the pairwise actions of the heterogeneous agents. Moreover, as a byproduct of our theoretical results, we show that a class of nonlinear voter models, recently the subject of increasing interest, called q-voter models, can be viewed as a replicator dynamic driven by a utility that is a power of the probability density. This implies that non-exchangeable and/or mean-field game formulations of these models can also be constructed. We also present computational examples of evolutionary and mean field game models using a finite difference method, focusing on tragedy of the commons and the q-voter model with non-exchangeable agents, of which are interesting cases from theoretical and computational perspectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-exchangeable evolutionary and mean field games and their applications Yoshioka, H. Tsujimura, M. Tanaka, T. Optimization and Control Numerical Analysis Probability A replicator dynamic for non-exchangeable agents in a continuous action space is formulated and its well-posedness is proven in a space of probability measures. The non-exchangeability allows for the analysis of evolutionary games involving agents with distinct (and possibly infinitely many) types. We also explicitly connect this replicator dynamic to a stationary mean field game, which determines the pairwise actions of the heterogeneous agents. Moreover, as a byproduct of our theoretical results, we show that a class of nonlinear voter models, recently the subject of increasing interest, called q-voter models, can be viewed as a replicator dynamic driven by a utility that is a power of the probability density. This implies that non-exchangeable and/or mean-field game formulations of these models can also be constructed. We also present computational examples of evolutionary and mean field game models using a finite difference method, focusing on tragedy of the commons and the q-voter model with non-exchangeable agents, of which are interesting cases from theoretical and computational perspectives. |
| title | Non-exchangeable evolutionary and mean field games and their applications |
| topic | Optimization and Control Numerical Analysis Probability |
| url | https://arxiv.org/abs/2506.02644 |