The Myopic Stable Set for Social Environments

Thomas Demuynck, P. Jean-Jacques Herings, Riccardo Saulle, Christian Seel

Research output: Working paperProfessional

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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 superset of the core and of the set of pure strategy Nash equilibria in noncooperative 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 supermodular 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.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
DOIs
Publication statusPublished - 2017

Publication series

SeriesGSBE Research Memoranda
Number002

JEL classifications

  • c70 - Game Theory and Bargaining Theory: General
  • c71 - Cooperative Games

Keywords

  • Social environments
  • group formation
  • stability
  • Nash equilibrium

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