Variational convergence: Approximation and existence of equilibria in discontinuous games

• 成果类型: Article
• 署名作者: Bagh, Adib
• 署名单位: University of Kentucky; University of Kentucky
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2010.01.009
• 发表日期: 2010
• 页码: 1244-1268
• 关键词: Convergence of games; discontinuous games; Equilibrium map; Bertrand-Edgeworth games

摘要

We introduce a notion of variational convergence for sequences of games and we show that the Nash equilibrium map is upper semi-continuous with respect to variationally converging sequences. We then show that for a game G with discontinuous payoff, some of the most important existence results of Dasgupta and Maskin, Simon, and Reny are based on constructing approximating sequences of games that variationally converge to G. In fact, this notion of convergence will help simplify these results and make their proofs more transparent. Finally, we use our notion of convergence to establish the existence of a Nash equilibrium for Bertrand-Edgeworth games with very general forms of tie-breaking and residual demand rules. (C) 2010 Elsevier Inc. All rights reserved.