Mean-field games of optimal stopping: master equation and weak equilibria
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911132357230592 |
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| author | Possamaï, Dylan Talbi, Mehdi |
| author_facet | Possamaï, Dylan Talbi, Mehdi |
| contents | We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly discussing the N-player game, we formulate the corresponding mean-field problem. In particular, we introduce a weak formulation of the game for which we are able to prove existence of Nash equilibria for a large class of criteria. We also prove that equilibria for the mean-field problem provide approximated Nash equilibria for the N-player game, and we formally derive the master equation associated with our mean-field game. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09278 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean-field games of optimal stopping: master equation and weak equilibria Possamaï, Dylan Talbi, Mehdi Probability Optimization and Control We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly discussing the N-player game, we formulate the corresponding mean-field problem. In particular, we introduce a weak formulation of the game for which we are able to prove existence of Nash equilibria for a large class of criteria. We also prove that equilibria for the mean-field problem provide approximated Nash equilibria for the N-player game, and we formally derive the master equation associated with our mean-field game. |
| title | Mean-field games of optimal stopping: master equation and weak equilibria |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2307.09278 |