A Note on Type-Symmetries in Finite Games

Renato Soeiro () and Alberto A. Pinto
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Renato Soeiro: INESC TEC, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Alberto A. Pinto: INESC TEC, Faculty of Sciences, University of Porto, Rua do Campo Alegre, s/n, 4169-007 Porto, Portugal

Mathematics, 2022, vol. 10, issue 24, 1-13

Abstract: In two-action generalized polymatrix games, Nash equilibria are support-type-symmetric, i.e., determined by supports for each type of player. We show that such a property does not generalize straightforwardly for games with at least three actions or where interaction weights have different signs (neither all positive nor negative). A non-trivial condition on interaction weights must be satisfied, which may go unnoticed as it is trivially satisfied for: (i) two-action games, (ii) conformity games, and (iii) congestion games. We derive this condition and the corresponding simplified analytic equation for mixed strategies.

Keywords: Nash equilibrium; type-symmetry; polymatrix games; non-cooperative games; network interactions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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