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

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  • Haake, Claus-Jochen

    (Center for Mathematical Economics, Bielefeld University)

  • Trockel, Walter

    (Center for Mathematical Economics, 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

  • Haake, Claus-Jochen & Trockel, Walter, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Center for Mathematical Economics Working Papers 647, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:647
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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.
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    5. 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.
    6. 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.
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    Keywords

    socio-legal systems; implementation; social systems; generalized games; Nash demand game;
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