Approximate Nash equilibrium under the single crossing conditions
AbstractWe 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 epsilon-optimization of a bounded-above 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 44320.
Date of creation: 10 Feb 2013
Date of revision:
strong acyclicity; single crossing; Cournot tatonnement; Nash equilibrium; aggregative game;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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