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Invariant equilibria and classes of equivalent games

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

Games and Economic Behavior, 2022, vol. 132, issue C, 448-462

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.

Keywords: Discontinuous games; Nash equilibrium; Invariance; Sharing rules; Existence of equilibria (search for similar items in EconPapers)
Date: 2022
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Working Paper: Invariant Equilibria and Classes of Equivalent Games (2018) Downloads
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DOI: 10.1016/j.geb.2022.01.011

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Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:448-462