The Existence of Equilibria in Discontinuous and Nonconvex Games
AbstractThis paper investigates the existence of pure strategy, dominant-strategy, and mixed strategy Nash equilibria in discontinuous and nonconvex games. We introduce a new notion of very weak continuity, called weak transfer continuity, which holds in a large class of discontinuous economic games and is easy to check. We show that it, together with the compactness of strategy space and the quasiconcavity of payoff functions, permits the existence of pure strategy Nash equilibria. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in Baye et al.  and Reny . We provide sufficient conditions for weak transfer continuity by introducing notions of weak transfer upper continuity and weak transfer lower continuity. These conditions are satisfied in many economic games and are often quite simple to check. We also introduce the notion of weak dominant transfer upper continuity, and use it to study the existence of dominant strategy equilibria. We then generalize these results and those in Baye et al.  and Reny  without assuming any form of quasi-concavity of payoff functions or convexity of strategy spaces.
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Bibliographic InfoPaper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-14.
Length: 34 pages
Date of creation: Nov 2008
Date of revision: Mar 2010
Nash equilibrium; dominant strategy equilibrium; discontinuity; nonquasiconcavity; nonconvexity and mixed strategy;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-10-31 (All new papers)
- NEP-GTH-2009-10-31 (Game Theory)
- NEP-MIC-2009-10-31 (Microeconomics)
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