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A Note on Type-Symmetries in Finite Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Renato Soeiro & Alberto A. Pinto, 2022. "A Note on Type-Symmetries in Finite Games," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4696-:d:1000131
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    References listed on IDEAS

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