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A sandwich theorem for generic n × n two person games
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 behaviorVolume
120Pagination
86 - 95Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0899-8256eISSN
1090-2473Language
engPublication classification
C1 Refereed article in a scholarly journalUsage metrics
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