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



Bich, P and Laraki, R ORCID: 0000-0002-4898-2424
(2017) On the existence of approximate equilibria and sharing rule solutions in discontinuous games. THEORETICAL ECONOMICS, 12 (01). pp. 79-108.

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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.

Item Type: Article
Uncontrolled Keywords: Discontinuous games, better-reply security, sharing rules, approximate equilibrium, Reny equilibrium, strategic approximation, auctions, timing games
Depositing User: Symplectic Admin
Date Deposited: 04 Oct 2017 11:42
Last Modified: 19 Jan 2023 06:53
DOI: 10.3982/TE2081
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3009769