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The Myopic Stable Set for Social Environments

Author

Listed:
  • Thomas Demuynck

    (Ecares, Université Libre de Bruxelles)

  • Jean-Jacques Herings

    (Department of Economics, Maastricht University)

  • Riccardo D. Saulle

    (Department of Economics, Maastricht University)

  • Christian Seel

    (Department of Economics, Maastricht University)

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.

Suggested Citation

  • Thomas Demuynck & Jean-Jacques Herings & Riccardo D. Saulle & Christian Seel, 2017. "The Myopic Stable Set for Social Environments," Working Papers 2017.26, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2017.26
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    2. Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Last will be First, and the First Last: Segregation in Societies with Positional Externalities," Research Memorandum 027, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2021. "Horizon- K Farsightedness in Criminal Networks," Games, MDPI, Open Access Journal, vol. 12(3), pages 1-13, July.
    4. Thomas Demuynck & P. Jean-Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "Bertrand competition with asymmetric costs: a solution in pure strategies," Theory and Decision, Springer, vol. 87(2), pages 147-154, September.
    5. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    6. Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.
    7. Agust'in G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "Non-convergence to stability in coalition formation games," Papers 2009.11689, arXiv.org.
    8. Herings, Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Do Stable Outcomes Survive in Marriage Problems with Myopic and Farsighted Players?," LIDAM Discussion Papers CORE 2020033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 0. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-35.
    10. Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2020. "The Last will be First, and the First Last: Segregation in Societies with Relative Payoff Concerns (RM/18/027-revised-)," Research Memorandum 011, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Herings, Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "Horizon-K Farsightedness in Criminal Networks," LIDAM Reprints CORE 3167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    Social Environments; Group Formation; Stability; Nash Equilibrium;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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