Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).

中文翻译：

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概率系统的理性验证

理性验证是在假设系统中的代理通过选择共同形成博弈论均衡的策略理性行动的情况下，确定哪些时间逻辑属性将适用于多代理系统的问题。该领域以前的工作主要集中在确定性系统上。在本文中，我们开发了概率系统中理性验证的理论和算法。我们专注于并发随机博弈 (CSG)，它可用于对复杂多智能体环境中的不确定性和随机性进行建模。我们在定性概率设置中研究非合作博弈和合作博弈的理性验证问题。在前一种情况下，我们考虑博弈的纳什均衡满足的 LTL 属性，在后一种情况下，核心满足 LTL 属性。在这两种情况下，我们都表明问题是 2EXPTIME-complete，因此并不比模型检查 LTL 属性的模型验证问题困难得多，该模型检查建模为马尔可夫决策过程 (MDP) 的系统的 LTL 属性。