The Myopic Stable Set for Social Environments

37 Pages Posted: 23 Jan 2017

See all articles by Thomas Demuynck

Thomas Demuynck

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES)

P. Jean-Jacques Herings

Maastricht University

Riccardo Saulle

Maastricht University

Christian Seel

Maastricht University

Multiple version iconThere are 3 versions of this paper

Date Written: December 21, 2016

Abstract

We introduce a new solution concept for models of coalition formation, called the myopic stable set. The myopic stable set is defined for a very general class of social environments and allows for an infinite state space. We show that the myopic stable set exists and is non-empty. Under minor continuity conditions, we also demonstrate uniqueness. Furthermore, the myopic stable set is a super-set of the core and of the set of pure strategy Nash equilibria in non-cooperative games.

Additionally, the myopic stable set generalizes and unifies various results from more specific environments. In particular, the myopic stable set coincides with the coalition structure core in coalition function form games if the coalition structure core is non-empty; with the set of stable matchings in the standard one-to-one matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in finite super-modular games, finite potential games, and aggregative games. We illustrate the versatility of our concept by characterizing the myopic stable set in a model of Bertrand competition with asymmetric costs, for which the literature so far has not been able to fully characterize the set of all (mixed) Nash equilibria.

Keywords: social environments, group formation, stability, Nash equilibrium

JEL Classification: C70, C71

Suggested Citation

Demuynck, Thomas and Herings, P. Jean-Jacques and Saulle, Riccardo and Seel, Christian, The Myopic Stable Set for Social Environments (December 21, 2016). Available at SSRN: https://ssrn.com/abstract=2902651 or http://dx.doi.org/10.2139/ssrn.2902651

Thomas Demuynck

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium

P. Jean-Jacques Herings (Contact Author)

Maastricht University ( email )

Department of Economics
P.O. Box 616
6200 MD Maastricht
Netherlands
+31 43 3883636 (Phone)
+31 43 3884878 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/p.herings/herings.htm

Riccardo Saulle

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200MD
Netherlands

Christian Seel

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200MD
Netherlands
0031 433883651 (Phone)

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