Theoretical Economics, Volume 12, Number 1 ( 2017)

Theoretical Economics 12 (2017), 79–108

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

Philippe Bich, Rida Laraki


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.

Keywords: Discontinuous games, better-reply security, sharing rules, approximate equilibrium, Reny equilibrium, strategic approximation, auctions, timing games

JEL classification: C02, C62, C72

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