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Strategic behavior in non-atomic games

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  • Barlo, Mehmet
  • Carmona, Guilherme

Abstract

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.

Suggested Citation

  • Barlo, Mehmet & Carmona, Guilherme, 2015. "Strategic behavior in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 134-144.
  • Handle: RePEc:eee:mateco:v:60:y:2015:i:c:p:134-144
    DOI: 10.1016/j.jmateco.2015.07.003
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    Cited by:

    1. Alioğulları, Zeynel Harun & Barlo, Mehmet, 2012. "Entropic selection of Nash equilibrium," MPRA Paper 37132, University Library of Munich, Germany.
    2. Carmona, Guilherme, 2003. "A Re-Interpretation of the Concept of Nash Equilibrium Based on the Notion of Social Institutions," FEUNL Working Paper Series wp425, Universidade Nova de Lisboa, Faculdade de Economia.
    3. Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia.
    4. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.
    5. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, EconWPA.
    6. Guilherme Carmona, 2004. "On the Existence of Equilibrium Bank Runs in a Diamond-Dybvig Environment," Finance 0404009, EconWPA.
    7. Carmona, Guilherme, 2007. "Bank failures caused by Large withdrawals: An explanation based purely on liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 818-841, September.
    8. Guilherme Carmona, 2003. "A Re-Interpretation of Nash Equilibrium Based on the Notion of Social Institutions," Game Theory and Information 0311005, EconWPA.

    More about this item

    Keywords

    Nash equilibrium; Strategic equilibrium; Games with a continuum of players; Equilibrium distributions;

    JEL classification:

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

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