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Entropic selection of Nash equilibrium

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  • Alioğulları, Zeynel Harun
  • Barlo, Mehmet

Abstract

This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence.

Suggested Citation

  • Alioğulları, Zeynel Harun & Barlo, Mehmet, 2012. "Entropic selection of Nash equilibrium," MPRA Paper 37132, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:37132
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    File URL: https://mpra.ub.uni-muenchen.de/37132/1/MPRA_paper_37132.pdf
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    References listed on IDEAS

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    1. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
    2. Barlo, Mehmet & Carmona, Guilherme, 2015. "Strategic behavior in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 134-144.
    3. Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    5. van Damme, E.E.C. & Kühn, H. & Harsanyi, J. & Selten, R. & Weibull, J. & Nash Jr., J. & Hammerstein, P., 1996. "The work of John Nash in game theory," Other publications TiSEM f84995ec-5162-4438-8ca3-8, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    Entropic Selection of Nash Equilibrium; Refinements of Nash Equilibrium;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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