Duman P, Trockel W. Nash Smoothing on the Test Bench: $H_{\alpha}$ -Essential Equilibria . Center for Mathematical Economics Working Papers. Vol 632. Bielefeld: Center for Mathematical Economics; 2020. ; 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 efficient 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 $H_{\alpha}$-essentiality. A special case of our result for α = 1/2 is $H_{1/2}$-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 diffeerence between the asymmetric Nash solutions and the symmetric one is that the latter one is symmetric. While our proofs are mathematically straightforward given the analysis of van Damme (1987), our results change drastically the prevalent interpretation of Nash's smoothing of his demand game and dilute its conceptual importance.


    Zugriff

    Download


    Exportieren, teilen und zitieren



    Titel :

    Nash Smoothing on the Test Bench: $H_{\alpha}$ -Essential Equilibria


    Beteiligte:
    Duman, Papatya (Autor:in) / Trockel, Walter (Autor:in)

    Erscheinungsdatum :

    2020-01-01


    Medientyp :

    Paper


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Klassifikation :

    DDC:    330 / 629




    Nash smoothing on the test bench: Hα-essential equilibria

    Duman, Papatya / Trockel, Walter | BASE | 2020

    Freier Zugriff


    Distributed Seeking of Nash Equilibria in Mobile Sensor Networks

    Stankovic, Milos S. / Johansson, Karl H. / Stipanovic, Dusan M. | BASE | 2010

    Freier Zugriff

    Against all Odds: Nash Equilibria in a Road Pricing Experiment

    Schneider, K. / Weimann, J. | British Library Conference Proceedings | 2004


    Interval methods for computing strong Nash equilibria of continuous games

    Kubica, Bartłomiej / Woźniak, Adam | BASE | 2016

    Freier Zugriff