In rational verification, the aim is to verify which temporal logic properties will obtain in a multi-agent system, under the assumption that agents (“players”) in the system choose strategies for acting that form a game theoretic equilibrium. Preferences are typically defined by assuming that agents act in pursuit of individual goals, specified as temporal logic formulae. To date, rational verification has been studied using non-cooperative solution concepts—Nash equilibrium and refinements thereof. Such non-cooperative solution concepts assume that there is no possibility of agents forming binding agreements to cooperate, and as such they are restricted in their applicability. In this article, we extend rational verification to cooperative solution concepts, as studied in the field of cooperative game theory. We focus on the core, as this is the most fundamental (and most widely studied) cooperative solution concept. We begin by presenting a variant of the core that seems well-suited to the concurrent game setting, and we show that this version of the core can be characterised using ATL^⁎. We then study the computational complexity of key decision problems associated with the core, which range from problems in PSpace to problems in 3ExpTime. We also investigate conditions that are sufficient to ensure that the core is non-empty, and explore when it is invariant under bisimilarity. We then introduce and study a number of variants of the main definition of the core, leading to the issue of credible deviations, and to stronger notions of collective stable behaviour. Finally, we study cooperative rational verification using an alternative model of preferences, in which players seek to maximise the mean-payoff they obtain over an infinite play in games where quantitative information is allowed.

在理性验证中，目的是在假设系统中的代理（“参与者”）选择形成博弈论均衡的行动策略的情况下，验证在多代理系统中将获得哪些时间逻辑属性。偏好通常通过假设代理人为追求个人目标而行动来定义，指定为时间逻辑公式。迄今为止，已经使用非合作解决方案概念——纳什均衡及其改进来研究理性验证。这种非合作解决方案的概念假设代理不可能形成有约束力的合作协议，因此它们的适用性受到限制。在本文中，我们将理性验证扩展到合作解决方案概念，如在合作博弈论领域研究的那样。我们专注于核心，因为这是最基本（也是研究最广泛）的合作解决方案概念。我们首先展示了一个似乎非常适合并发游戏设置的核心变体，并且我们展示了可以使用 ATL ^⁎来表征这个版本的核心。然后，我们研究了与核心相关的关键决策问题的计算复杂度，范围从PSpace中的问题到3ExpTime中的问题. 我们还调查了足以确保核心非空的条件，并探索了何时在双相似性下它是不变的。然后我们介绍和研究核心主要定义的一些变体，导致可信偏差问题，以及更强的集体稳定行为概念。最后，我们使用另一种偏好模型研究合作理性验证，其中玩家寻求最大化他们在允许定量信息的游戏中无限游戏中获得的平均收益。