Structural Relations of Symmetry among Players in Strategic Games

TL;DR

This paper introduces a combinatorial framework based on group actions to analyze symmetry and anonymity in strategic games, providing new characterizations of player roles and structural symmetries in payoff matrices.

Contribution

It develops a novel combinatorial approach to formalize and analyze symmetry notions in strategic games, including partial symmetries and player roles.

Findings

Defines a combinatorial framework using group actions for symmetry analysis

Introduces the concept of player roles and their relations in payoff matrices

Provides new characterizations of structural symmetries 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.