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A sandwich theorem for generic n × n two person games

journal contribution
posted on 01.03.2020, 00:00 authored by Ching-Jen SunChing-Jen Sun
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.

History

Journal

Games and economic behavior

Volume

120

Pagination

86 - 95

Publisher

Elsevier

Location

Amsterdam, The Netherlands

ISSN

0899-8256

eISSN

1090-2473

Language

eng

Publication classification

C1 Refereed article in a scholarly journal