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Nash Smoothing on the Test Bench: Ha-Essential Equilibria

Author

Listed:
  • Papatya Duman

    (Paderborn University)

  • Walter Trockel

    (Bielefeld University)

Abstract

We extend the analysis of van Damme (1987, Section 7.5) of the famous smoothing demand in Nash (1953) as an argument for the singular stability of the symmetric Nash bargaining solution among all Pareto ecient equilibria of the Nash demand game. Van Damme's analysis provides a clean mathematical framework where he substantiates Nash's conjecture by two fundamental theorems in which he proves that the Nash solution is among all Nash equilibria of the Nash demand game the only one that is H{essential. We show by generalizing this analysis that for any asymmetric Nash bargaining solution a similar stability property can be established that we call H {essentiality. A special case of our result for a = 1=2 is H1/2-essentiality that coincides with van Damme's H{essentiality. Our analysis deprives the symmetric Nash solution equilibrium of Nash's demand game of its exposed position and fortifies our conviction that, in contrast to the predominant view in the related literature, the only structural di erence between the asymmetric Nash solutions and the symmetric one is that the latter one is symmetric.

Suggested Citation

  • Papatya Duman & Walter Trockel, 2020. "Nash Smoothing on the Test Bench: Ha-Essential Equilibria," Working Papers CIE 130, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:130
    as

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    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP130.pdf
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    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    5. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.
    6. Kaneko, Mamoru, 1981. "A bilateral monopoly and the nash cooperative solution," Journal of Economic Theory, Elsevier, vol. 24(3), pages 311-327, June.
    7. Papatya Duman, 2020. "Does Informational Equivalence Preserve Strategic Behavior? Experimental Results on Trockel’s Model of Selten’s Chain Store Story," Games, MDPI, vol. 11(1), pages 1-24, February.
    8. Carlsson, Hans, 1991. "A Bargaining Model Where Parties Make Errors," Econometrica, Econometric Society, vol. 59(5), pages 1487-1496, September.
    9. David Malueg, 2010. "Mixed-strategy equilibria in the Nash Demand Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 243-270, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    2-person bargaining games; {symmetric Nash solution; Nash demand game; Nash smoothing of games; H {essential Nash equilibrium;
    All these keywords.

    JEL classification:

    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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