Linear Dynamic Logic on finite traces $({\mathrm{LDL}}_{\mathrm{F}})$ is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on ${\mathrm{LDL}}_{\mathrm{F}}$. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because ${\mathrm{LDL}}_{\mathrm{F}}$ goals are considered, in the settings we study—Reactive Modules games and iterated Boolean games with goals over finite traces—players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with ${\mathrm{LDL}}_{\mathrm{F}}$ objectives is regular, and provides complexity results for the associated automata constructions.

有限迹线上的线性动态逻辑$（{\mathrm{低密度脂蛋白}}_{\mathrm{F}}）$是用于推理并发和多代理系统行为的强大逻辑。在本文中，我们研究了使用基于逻辑的目标/目的表达的多人游戏中表征和验证均衡性的技术${\mathrm{低密度脂蛋白}}_{\mathrm{F}}$。这项研究基于布尔游戏的泛化，布尔游戏是一种多智能体系统的基于逻辑的游戏模型，其中玩家具有以逻辑方式简洁地表示目标的目标。因为${\mathrm{低密度脂蛋白}}_{\mathrm{F}}$在我们研究的设置中考虑目标（即反应性模块游戏和具有超过有限轨迹的目标的迭代布尔型游戏），可以将玩家的目标定义为常规属性，同时以有限但任意大的轨迹实现。特别是，使用交替自动机，研究了自动机理论方法来表征和验证（纯策略纳什）均衡，证明多玩家游戏中的纳什均衡集具有${\mathrm{低密度脂蛋白}}_{\mathrm{F}}$ 目标是有规律的，并为关联的自动机构造提供了复杂的结果。