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On the existence of essential and trembling-hand perfect equilibria in discontinuous games

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  • Vincenzo Scalzo

    (University of Napoli Federico II)

Abstract

We identify classes of discontinuous games with infinitely many pure strategies where, for every class and every game in a dense subset, any mixed-strategy equilibrium is essential. Moreover, in some cases, we prove that the essential mixed-strategy equilibria are trembling-hand perfect and each stable set of equilibria contains only one element.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:etbull:v:2:y:2014:i:1:d:10.1007_s40505-013-0021-5
    DOI: 10.1007/s40505-013-0021-5
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    References listed on IDEAS

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    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. Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    4. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    5. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    6. 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.
    7. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    8. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1993. "The Solution to the Tullock Rent-Seeking Game when R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 10-93-9, Pennsylvania State - Department of Economics.
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    12. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
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    Cited by:

    1. Vincenzo Scalzo, 2016. "Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 571-586, March.
    2. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.
    3. Ram Sewak Dubey & Francesco Ruscitti, 2015. "A remark on the continuity of the Walras correspondence in pure exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 33-41, April.

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    More about this item

    Keywords

    Discontinuous infinite games; Essential equilibria; Trembling-hand perfect equilibria; Strategic stability;
    All these keywords.

    JEL classification:

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

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