On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games
Bich, Philippe; Laraki, Rida (2017), On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games, Theoretical Economics, 12, 1, p. 79-108. 10.3982/TE2081
TypeArticle accepté pour publication ou publié
Journal nameTheoretical Economics
Society for Economic Theory
MetadataShow full item record
Centre d'économie de la Sorbonne [CES]
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)This paper studies the existence of some known 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, and its recent improvements. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models with discontinuous preferences have a sharing rule solution.
Subjects / KeywordsDiscontinuous games; better-reply security; sharing rules; approximate equilibrium; Reny equilibrium; strategic approximation; auctions; timing games
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