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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 (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 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 (J Math Econ 2(3):345–348, 1975) that also generalizes the dc-mechanism of Koray and Yildiz (J Econ Theory 176:479–502, 2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (Designing rights: invisible hand theorems, covering and membership. Tech. rep. Mimeo, Bogazici University, 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, 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.
    • Handle: RePEc:spr:reecde:v:26:y:2022:i:4:d:10.1007_s10058-021-00278-z
    DOI: 10.1007/s10058-021-00278-z
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    References listed on IDEAS

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    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. Koray, Semih & Yildiz, Kemal, 2018. "Implementation via rights structures," Journal of Economic Theory, Elsevier, vol. 176(C), pages 479-502.
    7. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    8. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    9. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    10. 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.
    11. 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.
    12. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
    13. Prakash, Prem & Sertel, Murat R., 1996. "Existence of non-cooperative equilibria in social systems," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 19-32.
    14. 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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    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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