Abstract In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in pursuit of individual objectives. Typically, those objectives are expressed as temporal logic formulae which the relevant agent desires to see satisfied. Unfortunately, rational verification is computationally complex, and requires specialised techniques in order to obtain practically useable implementations. In this paper, we present such a technique. This technique relies on a reduction of the rational verification problem to the solution of a collection of parity games. Our approach has been implemented in the Equilibrium Verification Environment ( EVE ) system. The EVE system takes as input a model of a concurrent/multi-agent system represented using the Simple Reactive Modules Language (SRML), where agent goals are represented as Linear Temporal Logic ( ) formulae, together with a claim about the equilibrium behaviour of the system, also expressed as an formula. EVE can then check whether the claim holds on some (or every) computation of the system that could arise through agents choosing Nash equilibrium strategies; it can also check whether a system has a Nash equilibrium, and synthesise individual strategies for players in the multi-player game. After presenting our basic framework, we describe our new technique and prove its correctness. We then describe our implementation in the EVE system, and present experimental results which show that EVE performs favourably in comparison to other existing tools that support rational verification.

中文翻译：

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自动时间均衡分析：多人游戏的验证和综合

摘要 在多代理系统的背景下，理性验证问题涉及检查当系统的组成代理被假定为追求个人目标而理性和战略性地行为时，系统中将保持哪些时间逻辑属性。通常，这些目标表示为相关代理希望看到满足的时间逻辑公式。不幸的是，理性验证在计算上很复杂，需要专门的技术才能获得实际可用的实现。在本文中，我们介绍了这样一种技术。该技术依赖于将理性验证问题简化为一组奇偶游戏的解决方案。我们的方法已在均衡验证环境 (EVE) 系统中实施。EVE 系统将使用简单反应模块语言 (SRML) 表示的并发/多代理系统模型作为输入，其中代理目标表示为线性时间逻辑 ( ) 公式，以及有关均衡行为的声明系统，也用公式表示。然后，EVE 可以检查该声明是否适用于系统的某些（或每个）计算，这些计算可能通过代理选择纳什均衡策略而产生；它还可以检查系统是否存在纳什均衡，并在多人游戏中为玩家合成个人策略。在介绍了我们的基本框架之后，我们描述了我们的新技术并证明了它的正确性。然后我们描述我们在 EVE 系统中的实现，