Nessah, Rabia and Tian, Guoqiang (2008): Existence of Equilibria in Discontinuous Games.

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Abstract
This paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous games. We introduce a new notion of weak continuity, called weak transfer quasicontinuity, which is weaker than most known weak notions of continuity, including diagonal transfer continuity in Baye et al (1993) and betterreply security in Reny (1999), and holds in a large class of discontinuous games. We show that it, together with strong diagonal transfer quasiconcavity introduced in the paper, is enough to guarantee the existence of Nash equilibria in compact and convex normal form games. We provide sufficient conditions for weak transfer quasicontinuity by introducing notions of weak transfer continuity, weak transfer upper continuity, and weak transfer lower continuity. Moreover, an analogous analysis is applied to show the existence of dominant strategy and mixed strategy Nash equilibria in discontinuous games.
Item Type:  MPRA Paper 

Original Title:  Existence of Equilibria in Discontinuous Games 
Language:  English 
Keywords:  Discontinuous games, weak transfer quasicontinuity, pure strategy, mixed strategy, dominant strategy, Nash equilibrium, existence 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C70  General 
Item ID:  41206 
Depositing User:  Guoqiang Tian 
Date Deposited:  12. Sep 2012 12:49 
Last Modified:  12. Feb 2013 12:09 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/41206 