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Integrating the Nash program into mechanism theory

Author

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  • Trockel, Walter

    (Center for Mathematical Economics, Bielefeld University)

Abstract
The present paper provides a method by which the Nash Program may be embedded into mechanism theory. It is shown that any result stating the support of any solution of a cooperative game in coalitional form by a Nash equilibrium of some suitable game in strategic form can be used to derive the mechanism theoretic Nash-implementation of that solution.
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Suggested Citation

  • Trockel, Walter, 2017. "Integrating the Nash program into mechanism theory," Center for Mathematical Economics Working Papers 305, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:305
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    File URL: https://pub.uni-bielefeld.de/download/2909882/2910106
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    References listed on IDEAS

    as
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    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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    5. Jackson, Matthew O. & Palfrey, Thomas R., 2001. "Voluntary Implementation," Journal of Economic Theory, Elsevier, vol. 98(1), pages 1-25, May.
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    13. Walter Trockel, 2002. "A universal meta bargaining implementation of the Nash solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 581-586.
    14. Trockel, Walter, 2017. "A universal meta bargaining realization of the Nash solution," Center for Mathematical Economics Working Papers 310, Center for Mathematical Economics, Bielefeld University.
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    20. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
    21. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    22. William Thomson, 1996. "Concepts Of Implementation," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 133-143, June.
    23. Haake, Claus-Jochen, 2017. "Implementation of the Kalai Smorodinski bargaining solution in dominant strategies," Center for Mathematical Economics Working Papers 301, Center for Mathematical Economics, Bielefeld University.
    24. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
    25. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    26. Trockel, Walter, 1996. "An Exact Implementation of the Nash Bargaining Solution in Dominant Strategies," Economics Series 25, Institute for Advanced Studies.
    27. Trockel, Walter, 2017. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.
    28. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
    29. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    30. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
    31. 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.
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    Cited by:

    1. 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.
    2. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    3. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    4. 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.
    5. 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.
    6. Hannu Vartiainen, 2007. "Nash implementation and the bargaining problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 333-351, September.
    7. Kang Rong, 2018. "Fair Allocation When Players' Preferences Are Unknown," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 497-509, January.
    8. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.
    9. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics.
    10. 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.
    11. 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.
    12. Trockel, Walter, 2017. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.

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