Kukushkin, Nikolai S. (2013): Approximate Nash equilibrium under the single crossing conditions.

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Abstract
We consider strategic games where strategy sets are linearly ordered while the preferences of the players are described by binary relations. All restrictions imposed on the preferences are satisfied in the case of epsilonoptimization of a boundedabove utility function. A Nash equilibrium exists and can be reached from any strategy profile after a finite number of best response improvements if the single crossing conditions hold w.r.t.\ pairs [one player's strategy, a profile of other players' strategies], and the preference relations are transitive. If, additionally, there are just two players, every best response improvement path reaches a Nash equilibrium after a finite number of steps. If each player is only affected by a linear combination of the strategies of others, the single crossing conditions hold w.r.t.\ pairs [one player's strategy, an aggregate of the strategies of others], and the preference relations are interval orders, then a Nash equilibrium exists and can be reached from any strategy profile with a finite best response path.
Item Type:  MPRA Paper 

Original Title:  Approximate Nash equilibrium under the single crossing conditions 
Language:  English 
Keywords:  strong acyclicity; single crossing; Cournot tatonnement; Nash equilibrium; aggregative game 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  44320 
Depositing User:  Nikolai S. Kukushkin 
Date Deposited:  10 Feb 2013 17:16 
Last Modified:  30 Sep 2019 15:22 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/44320 