Similarity as an extension of symmetry and its application to superrationality

Abstract In this paper we present a concept of similarity in games, on which to ground alternative solution concepts, some of which differ from the classical notions in the field. In order to do this we impose a constraint on players’ beliefs that amounts to a variant of the well-known symmetry principle in classical bargaining theory. We show how this similarity relation helps to identify different Nash equilibria in games, and how these “similar Nash equilibria” can be extended to non-symmetric games. While the notion is normative, it is nonetheless inspired by phenomena in which similarities between players lead to outcomes detected in behavioral studies. We study the strategic properties of the concept of similarity and discuss its relationships with Hofstadter’ notion of superrationality.摘要 本文提出了博弈中的相似性概念，并以此为基础构建替代性解概念，其中部分解概念与该领域的经典认知存在差异。为此，我们对参与者的信念施加约束，该约束等价于经典议价理论中广为人知的对称性原则的一种变体形式。本文阐明了该相似性关系如何帮助识别博弈中的各类纳什均衡，以及这类"相似纳什均衡"如何拓展至非对称博弈场景。尽管该概念属于规范性框架，但它的灵感来源于行为研究中观测到的、参与者间相似性催生相应结果的相关现象。本文研究了相似性概念的策略性质，并探讨了其与霍夫施塔特（Hofstadter）提出的超理性（superrationality）概念之间的关联。