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Core-equivalence for the Nash bargaining solution

Author

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  • Trockel, Walter

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Core equivalence and shrinking of the core results are well known for economies. The present paper establishes counterparts for bargaining economies, a specific class of production economies (finite and infinite) representing standard two-person bargaining games and their continuum counterparts as coalition production economies. Thereby we get core equivalence of the Nash solution. The results reconfirm the Walrasian approach to Nash bargaining of Trockel (1996). Moreover we establish the same speed of convergence as is known from Debreu (1975) and Grodal (1975) for replicated pure exchange economies and for regular purely competitive sequences of economies, respectively.

Suggested Citation

  • Trockel, Walter, 2011. "Core-equivalence for the Nash bargaining solution," Center for Mathematical Economics Working Papers 355, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:355
    as

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    File URL: https://pub.uni-bielefeld.de/download/2315394/2319782
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    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Grodal, Birgit, 1975. "The rate of convergence of the core for a purely competitive sequence of economies," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 171-186.
    3. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    4. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    5. Debreu, Gerard, 1975. "The rate of convergence of the core of an economy," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 1-7, March.
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    Keywords

    Nash solution; Core equivalence; Core convergence;
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