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On strategic stability in discontinuous games

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  • Carbonell-Nicolau, Oriol

Abstract

We identify a class of discontinuous normal-form games whose members possess strategically stable sets, defined according to an infinite-game extension of Kohlberg and Mertens’s (1986) equilibrium concept, and show that, generically, a set is stable if and only if it contains a single Nash equilibrium.

Suggested Citation

  • Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    • Handle: RePEc:eee:ecolet:v:113:y:2011:i:2:p:120-123
    DOI: 10.1016/j.econlet.2011.06.007
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    References listed on IDEAS

    as
    1. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, vol. 2(3), pages 1-22, July.
    2. Yong-Hui Zhou & Jian Yu & Shu-Wen Xiang, 2007. "Essential stability in games with infinitely many pure strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 493-503, April.
    3. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    4. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    5. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    6. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    8. Al-Najjar, Nabil, 1995. "Strategically stable equilibria in games with infinitely many pure strategies," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 151-164, April.
    9. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    10. Carbonell-Nicolau, Oriol, 2011. "On the existence of pure-strategy perfect equilibrium in discontinuous games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 23-48, January.
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    Cited by:

    1. Vincenzo Scalzo, 2014. "On the existence of essential and trembling-hand perfect equilibria in discontinuous games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 1-12, April.
    2. Carbonell-Nicolau, Oriol, 2011. "Perfect and limit admissible perfect equilibria in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 531-540.
    3. , & , P., 2014. "Refinements of Nash equilibrium in potential games," Theoretical Economics, Econometric Society, vol. 9(3), September.
    4. Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
    5. Norman, Thomas W.L., 2018. "Inefficient stage Nash is not stable," Journal of Economic Theory, Elsevier, vol. 178(C), pages 275-293.
    6. Oriol Carbonell-Nicolau & Richard McLean, 2015. "On equilibrium refinements in supermodular games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 869-890, November.

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    More about this item

    Keywords

    Infinite game; Normal-form game; Strategic stability; Trembling-hand perfect equilibrium;
    All these keywords.

    JEL classification:

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

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