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Invariant equilibria and classes of equivalent games

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  • Allison, Blake A.
  • Bagh, Adib
  • Lepore, Jason J.

Abstract

We consider classes of games for a fixed set of players with fixed strategy sets. For such classes, we analyze and develop the concept of invariance, which is satisfied when the set of Nash equilibria and corresponding equilibrium payoffs are identical for each payoff function within the class. We introduce the condition superior payoff matching, which requires that at any given strategy profile, each player can match her highest payoff near that strategy profile across all games within that class. If a specific game satisfies superior payoff matching, then its equilibria are invariant within a class of games with smaller sets of discontinuities. This condition can be used to prove existence of Nash equilibrium in games that are not quasiconcave or better reply secure.

Suggested Citation

  • Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:448-462
    DOI: 10.1016/j.geb.2022.01.011
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    2. Haimanko, Ori, 2024. "Bayesian Nash equilibrium in all-pay auctions with interdependent types," Games and Economic Behavior, Elsevier, vol. 146(C), pages 222-233.

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