A sandwich theorem for generic n × n two person games

Ching-jen Sun

Games and Economic Behavior, 2020, vol. 120, issue C, 86-95

Abstract: We study the structure of Nash equilibria in generic n×n games. A game is said to have a sandwich structure in Nash equilibria if there is a mixed strategy Nash equilibrium “inside” every collection of pure strategy Nash equilibria. A sufficient condition, which solely relies on the ordinal information of the game, is given for a generic n×n game to have a sandwich structure in Nash equilibria. We provide a lower bound on the number of Nash equilibria and determine the stability of each equilibrium in games with a sandwich structure in Nash equilibria. Moreover, when the number of pure strategy Nash equilibria is equal to the number of pure strategies available to each player, the exact structure of Nash equilibria can be determined.

Keywords: Nash equilibrium; Lefschetz-Hopf theorem; Index; Stability (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:120:y:2020:i:c:p:86-95

DOI: 10.1016/j.geb.2019.12.004

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