We study the memory requirements of Nash equilibria in turn-based multiplayer games on possibly infinite graphs with reachability, safety, shortest-path, Büchi and co-Büchi objectives. We present constructions for finite-memory Nash equilibria in these games that apply to arbitrary game graphs, bypassing the finite-arena requirement that is central in existing approaches. We show that, for these five types of games, from any Nash equilibrium, we can derive another Nash equilibrium where all strategies are finite-memory such that all objectives satisfied by the outcome of the original equilibrium also are by the outcome of the derived equilibrium, without increasing costs for shortest-path games. Furthermore, we provide memory bounds that are independent of the size of the game graph for reachability, safety and shortest-path games. These bounds depend only on the number of players. To the best of our knowledge, we provide the first results pertaining to finite-memory constrained Nash equilibria in infinite arenas and the first arena-independent memory bounds for Nash equilibria.

翻译：本文研究了在可能无限的图上进行的回合制多人博弈中，纳什均衡对记忆的需求，这些博弈的目标包括可达性、安全性、最短路径、Büchi 和 co-Büchi 目标。我们针对这些博弈提出了有限记忆纳什均衡的构造方法，这些方法适用于任意博弈图，绕过了现有方法中核心的有限竞技场要求。我们证明，对于这五类博弈，从任意一个纳什均衡出发，我们都可以推导出另一个纳什均衡，其中所有策略都是有限记忆的，并且原均衡结果所满足的所有目标，在推导出的均衡结果中同样得到满足，同时对于最短路径博弈不会增加成本。此外，我们为可达性、安全性和最短路径博弈提供了与博弈图规模无关的记忆界限。这些界限仅取决于玩家的数量。据我们所知，我们首次给出了无限竞技场中有限记忆约束纳什均衡的相关结果，以及纳什均衡的首个与竞技场无关的记忆界限。