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Implementations of the Nash solution based on its Walrasian characterization

Author

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  • Walter Trockel

    (Institute of Mathematical Economics, University of Bielefeld, Postfach 10 01 31, 33501 Bielefeld, GERMANY)

Abstract

The present paper provides three different support results for the Nash bargaining solution of $n$-person bargaining games. First, for any bargaining game there is defined a non-cooperative game in strategic form, whose unique Nash equilibrium induces a payoff vector that coincides with the Nash solution of the bargaining game. Next this game is modified in such a way that the unique Nash equilibrium that supports the Nash solution is even in dominant strategies. After that an $n$-stage game in extensive form is presented whose unique subgame perfect equilibrium supports the Nash solution of the bargaining game. Finally, the support results are shown to induce implementation results in the sense of mechanism theory.

Suggested Citation

  • Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 277-294.
    • Handle: RePEc:spr:joecth:v:16:y:2000:i:2:p:277-294
    Note: Received: October 3, 1999; revised version: October 26, 1999
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    Citations

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    Cited by:

    1. Trockel, Walter, 2017. "Can and should the Nash Program be looked at as a part of mechanism theory," Center for Mathematical Economics Working Papers 322, Center for Mathematical Economics, Bielefeld University.
    2. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    3. Claus-Jochen Haake & Walter Trockel, 2020. "Introduction to the Special Issue “Bargaining”," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 1-6, November.
    4. Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, vol. 77(2), pages 223-236, August.
    5. Brangewitz, Sonja & Gamp, Jan-Philip, 2016. "Inner Core, Asymmetric Nash Bargaining Solutions and Competitive Payoffs," Center for Mathematical Economics Working Papers 453, Center for Mathematical Economics, Bielefeld University.
    6. Claus-Jochen Haake & Walter Trockel, 2022. "Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 635-649, December.
    7. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    8. Haake, Claus-Jochen, 2009. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 177-187, March.
    9. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
    10. Matthias Dahm & Nicolas Porteiro, 2005. "A Micro- Foundation for Non-Deterministic Contests of the Logit Form," Discussion Papers 1410, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Thorsten Upmann & Julia Müller, 2014. "The Structure of Firm-Specific Labour Unions," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 170(2), pages 336-364, June.
    12. Trockel, Walter, 2017. "Integrating the Nash program into mechanism theory," Center for Mathematical Economics Working Papers 305, Center for Mathematical Economics, Bielefeld University.
    13. 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.
    14. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.

    More about this item

    Keywords

    Nash solution; Nash-implementation; Mechanism; Walrasian equilibrium.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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