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 groundalternative solution concepts, some of which differ from the classical notions in the field. Inorder to do this we impose a constraint on players´ beliefs that amounts to a variant of thewell-known symmetry principle in classical bargaining theory. We show how this similarityrelation helps to identify different Nash equilibria in games, and how these "similar Nashequilibria" can be extended to non-symmetric games. While the notion is normative, it isnonetheless inspired by phenomena in which similarities between players lead to outcomesdetected in behavioral studies. We study the strategic properties of the concept of similarityand discuss its relationships with Hofstadter´ notion of superrationality.