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Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium

Author

Listed:
  • Claus-Jochen Haake

    (Paderborn University)

  • Walter Trockel

    (Bielefeld University)

Abstract

In this article we combine Debreu's (1952) social system with Hurwicz's (1994, 2008) ideas of embedding a "desired" game form into a "natural" game form that includes all feasible behavior, even if it is "illegal" according to the desired form. For the resulting socio-legal system we extend Debreu's concepts of a social system and its social equilibria to a socio-legal system with its Debreu-Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (1975) that also generalizes the dc-mechanism of Koray and Yildiz (2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two-person cooperative bargaining. There we provide in a socio-legal system based on Nash's demand game an implementation of the Nash bargaining solution in Debreu-Hurwicz equilibrium.

Suggested Citation

  • Claus-Jochen Haake & Walter Trockel, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Working Papers CIE 140, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:140
    as

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    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP140.pdf
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    References listed on IDEAS

    as
    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. Wayne Shafer & Hugo Sonnenschein, 1976. "Equilibrium with Externalities," Discussion Papers 145, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
    4. 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.
    5. 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.
    6. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    7. Shafer, Wayne & Sonnenschein, Hugo, 1976. "Equilibrium with Externalities, Commodity Taxation, and Lump Sum Transfers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 601-611, October.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    socio-legal systems; implementation; social systems; generalized games; Nash demand game;
    All these keywords.

    JEL classification:

    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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