On the existence of approximate equilibria and sharing rule solutions in discontinuous games

• 成果类型: Article
• 署名作者: Bich, Philippe; Laraki, Rida
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Paris School of Economics; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE2081
• 发表日期: 2017-01-01
• 页码: 79-108
• 关键词: Discontinuous games; better-reply security; sharing rules; approximate equilibrium; Reny equilibrium; strategic approximation; auctions; timing games

摘要

This paper studies the existence of equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition (Reny, 1999) and its recent improvements (Barelli and Meneghel, 2013, McLennan et al.., 2011, Reny 2009, 2011). We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of approximate equilibria and of sharing rule solutions in pure and mixed strategies (Simon and Zame, 1990). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models have a sharing rule solution.