We study the memory requirements of Nash equilibria in turn-based multiplayer games on possibly infinite graphs with reachability, shortest path and B\"uchi 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 three types of games, from any Nash equilibrium, we can derive another Nash equilibrium where all strategies are finite-memory such that the same players accomplish their objective, without increasing their cost for shortest path games. Furthermore, we provide memory bounds that are independent of the size of the game graph for reachability 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：我们研究了在可能无限图上进行的回合制多人博弈中纳什均衡的内存需求，这些博弈涉及可达性、最短路径和Büchi目标。我们针对这些博弈构造了有限内存纳什均衡，该构造适用于任意博弈图，绕过了现有方法中至关重要的有限竞技场要求。我们证明，对于这三类博弈，从任意纳什均衡出发，可以推导出另一个所有策略均为有限内存的纳什均衡，使得相同玩家实现其目标，且不增加其在最短路径博弈中的成本。此外，我们为可达性和最短路径博弈提供了与博弈图大小无关的内存界，这些界仅依赖于玩家数量。据我们所知，这是首个关于无限竞技场中有限内存约束纳什均衡的结果，也是首个纳什均衡的无关于竞技场的内存界。