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

Bich, Philippe; Laraki, Rida

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

Type

Article accepté pour publication ou publié

Date

2017

Journal name

Theoretical Economics

Volume

Number

Publisher

Society for Economic Theory

Pages

79-108

Centre d'économie de la Sorbonne [CES]
Laraki, Rida

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 / Keywords

Discontinuous games; better-reply security; sharing rules; approximate equilibrium; Reny equilibrium; strategic approximation; auctions; timing games

JEL

C72 - Noncooperative Games
C62 - Existence and Stability Conditions of Equilibrium
C02 - Mathematical Methods