Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Ramit Das, R. Ramanujam, Sunil Simon
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Abstract

Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).
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一元不动点逻辑下的社会选择与博弈推理
无论是在正常形式的游戏中,还是在公平分配中,还是在投票系统中的选民偏好中,某种推理模式都是常见的。从一个特定的配置文件,一个代理或一组代理可能有动机转移到一个新的配置文件。这引出了一个自然的图结构,我们称之为这些系统策略空间上的改进图。我们认为带计数的一元不动点逻辑是带不动点和计数量词的图上一元一阶逻辑的扩展,是改进图上的一种自然规范语言,因此是一类可以跨这些域解释的属性的规范语言。该逻辑具有高效的模型检查算法(在改进图的大小上)。
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