Permissive Equilibria in Multiplayer Reachability Games
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910706013569024 |
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| author | Goeminne, Aline Monmege, Benjamin |
| author_facet | Goeminne, Aline Monmege, Benjamin |
| contents | We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are consistent with it. We aim for profiles of multi-strategies (a multi-strategy per player), where each profile of consistent strategies is a Nash equilibrium, or a subgame perfect equilibrium. The permissiveness of two multi-strategies can be compared with penalties, as already used in the two-player zero-sum setting by Bouyer, Duflot, Markey and Renault. We show that we can decide the existence of a multi-strategy that is a Nash equilibrium or a subgame perfect equilibrium, while satisfying some upper-bound constraints on the penalties in PSPACE, if the upper-bound penalties are given in unary. The same holds when we search for multi-strategies where certain players are asked to win in at least one play or in all plays |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Permissive Equilibria in Multiplayer Reachability Games Goeminne, Aline Monmege, Benjamin Computer Science and Game Theory We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are consistent with it. We aim for profiles of multi-strategies (a multi-strategy per player), where each profile of consistent strategies is a Nash equilibrium, or a subgame perfect equilibrium. The permissiveness of two multi-strategies can be compared with penalties, as already used in the two-player zero-sum setting by Bouyer, Duflot, Markey and Renault. We show that we can decide the existence of a multi-strategy that is a Nash equilibrium or a subgame perfect equilibrium, while satisfying some upper-bound constraints on the penalties in PSPACE, if the upper-bound penalties are given in unary. The same holds when we search for multi-strategies where certain players are asked to win in at least one play or in all plays |
| title | Permissive Equilibria in Multiplayer Reachability Games |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2411.13296 |