基于自动机的游戏与ω-自动偏好
An Automata-Based Approach to Games with $ω$-Automatic Preferences
AI总结：
本文提出基于自动机的多玩家回合制游戏方法，通过ω-自动关系建模玩家偏好，并研究价值与最优策略的计算复杂性，揭示合作理性合成的PSPACE完全性及非合作情况下的不可判定性。
摘要：
本文研究了在图上进行的多玩家回合制游戏，其中玩家偏好被建模为由确定性配对自动机给出的ω-自动关系。这与现有大多数工作不同，后者专注于特定的奖励函数。我们对这些游戏进行了计算分析，从对抗性零和情况下的阈值问题开始。如同经典游戏一样，我们引入了价值的概念，这里定义为玩家可以保证改善的play集合，相对于其偏好关系。我们证明该集合由一个多项式大小的交替配对自动机APW识别。我们还建立了与价值和最优策略概念相关的若干问题的计算复杂性，利用价值的ω-自动特性。接下来，我们转向多玩家游戏和纳什均衡，并在这一背景下重新审视阈值问题。基于再次使用APW构造，我们填补了文献中留下的复杂性空白，并进一步证明合作理性合成是PSPACE完全的，而在非合作情况下则变得不可判定。
英文摘要：
This paper studies multiplayer turn-based games on graphs in which player preferences are modeled as $ω$-automatic relations given by deterministic parity automata. This contrasts with most existing work, which focuses on specific reward functions. We conduct a computational analysis of these games, starting with the threshold problem in the antagonistic zero-sum case. As in classical games, we introduce the concept of value, defined here as the set of plays a player can guarantee to improve upon, relative to their preference relation. We show that this set is recognized by an alternating parity automaton APW of polynomial size. We also establish the computational complexity of several problems related to the concepts of value and optimal strategy, taking advantage of the $ω$-automatic characterization of value. Next, we shift to multiplayer games and Nash equilibria, and revisit the threshold problem in this context. Based on an APW construction again, we close complexity gaps left open in the literature, and additionally show that cooperative rational synthesis is $\mathsf{PSPACE}$-complete, while it becomes undecidable in the non-cooperative case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
