Concurrent stochastic games (CSGs) are an ideal formalism for modelling probabilistic systems that feature multiple players or components with distinct objectives making concurrent, rational decisions. Examples include communication or security protocols and multi-robot navigation. Verification methods for CSGs exist but are limited to scenarios where agents or players are grouped into two coalitions, with those in the same coalition sharing an identical objective. In this paper, we propose multi-coalitional verification techniques for CSGs. We use subgame-perfect social welfare (or social cost) optimal Nash equilibria, which are strategies where there is no incentive for any coalition to unilaterally change its strategy in any game state, and where the total combined objectives are maximised (or minimised). We present an extension of the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to specify equilibria-based properties for any number of distinct coalitions, and a corresponding model checking algorithm for a variant of stopping games. We implement our techniques in the PRISM-games tool and apply them to several case studies, including a secret sharing protocol and a public good game.

中文翻译：

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并发随机博弈的多人均衡验证

并发随机博弈 (CSG) 是建模概率系统的理想形式，该系统具有多个参与者或组件，这些参与者或组件具有不同的目标，可以做出并发、理性的决策。示例包括通信或安全协议以及多机器人导航。CSG 的验证方法存在，但仅限于将代理或参与者分组为两个联盟的场景，同一联盟中的那些共享相同的目标。在本文中，我们提出了 CSG 的多联盟验证技术。我们使用子博弈完美社会福利（或社会成本）最优纳什均衡，这些策略在任何博弈状态下都没有激励任何联盟单方面改变其策略，并且总组合目标最大化（或最小化）。我们提出了时间逻辑 rPATL（带奖励的概率交替时间时间逻辑）的扩展，以指定任意数量不同联盟的基于均衡的属性，以及用于停止游戏变体的相应模型检查算法。我们在 PRISM-games 工具中实现了我们的技术，并将它们应用于几个案例研究，包括一个秘密共享协议和一个公益游戏。