On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games

Philippe Bich () and Rida Laraki ()
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Philippe Bich: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Rida Laraki: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, X - École polytechnique - IP Paris - Institut Polytechnique de Paris

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Abstract: 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.

Keywords: Reny equilibrium; approximate equilibrium; timing games; strategic approximation; auctions; Discontinuous games; better-reply security; sharing rules (search for similar items in EconPapers)
Date: 2017-01-30
Note: View the original document on HAL open archive server: https://hal.science/hal-01396183v1
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Citations: View citations in EconPapers (11)

Published in Theoretical Economics, 2017, 12 (1), pp.79-108. ⟨10.3982/TE2081⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01396183

DOI: 10.3982/TE2081

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