Structural relations of symmetry among players in strategic games

Abstract

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.

Game-Theoretic Models of Moral and Other-Regarding Agents (extended abstract)

“…Notions of symmetry in games have been insufficiently investigated, and they play an important role in defining Kantian programs. We refer to [33,67] for such studies.…”

“…In this section we give a somewhat more general definition 10 of Kantian equilibria, but not for general games, only for a class of "symmetric" games. There are multiple definitions of game symmetry in the literature [33,67]; the most important one requires that for every player i, action profile (x 1 , x 2 , . .…”