The Myopic Stable Set for Social Environments
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 infinite 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.
|Date of creation:||Jan 2017|
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- Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590 Elsevier.
- Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017.
"Stable sets in matching problems with coalitional sovereignty and path dominance,"
Journal of Mathematical Economics,
Elsevier, vol. 71(C), pages 14-19.
- Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, "undated". "Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance," Research Memorandum 020, Maastricht University, Graduate School of Business and Economics (GSBE).
- HERINGS, P. Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, 2016. "Stable Sets in Matching Problems with Coalitional Sovereignty and Path Dominance," CORE Discussion Papers 2016010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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