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Inner Core, Asymmetric Nash Bargaining Solutions and Competitive Payoffs

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  • Sonja Brangewitz

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Jan-Philip Gamp

    ()
    (Institute of Mathematical Economics, Bielefeld University)

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    Abstract

    We investigate the relationship between the inner core and asymmetric Nash bargaining solutions for n-person bargaining games with complete information. We show that the set of asymmetric Nash bargaining solutions for different strictly positive vectors of weights coincides with the inner core if all points in the underlying bargaining set are strictly positive. Furthermore, we prove that every bargaining game is a market game. By using the results of Qin (1993) we conclude that for every possible vector of weights of the asymmetric Nash bargaining solution there exists an economy that has this asymmetric Nash bargaining solution as its unique competitive payoff vector. We relate the literature of Trockel (1996, 2005) with the ideas of Qin (1993). Our result can be seen as a market foundation for every asymmetric Nash bargaining solution in analogy to the results on non-cooperative foundations of cooperative games.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-453.pdf
    File Function: First version, 2011
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 453.

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    Length: 28 pages
    Date of creation: Aug 2011
    Date of revision:
    Handle: RePEc:bie:wpaper:453

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    Related research

    Keywords: Inner Core; Asymmetric Nash Bargaining Solution; Competitive Payoffs; Market Games;

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    1. Qin Cheng-Zhong, 1994. "The Inner Core of an n-Person Game," Games and Economic Behavior, Elsevier, vol. 6(3), pages 431-444, May.
    2. de Clippel, Geoffroy & Minelli, Enrico, 2005. "Two remarks on the inner core," Games and Economic Behavior, Elsevier, vol. 50(2), pages 143-154, February.
    3. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer, Springer, vol. 16(2), pages 277-294.
    4. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    5. Trockel,W., 2003. "Core-equivalence for the Nash bargaining solution," Working Papers 355, Bielefeld University, Center for Mathematical Economics.
    6. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, Econometric Society, vol. 78(5), pages 1593-1623, 09.
    7. Sun, N. & Trockel, W. & Yang, Z.F., 2004. "Competitive Outcomes and Endogenous Coalition Formation in an n-Person Game," Discussion Paper, Tilburg University, Center for Economic Research 2004-93, Tilburg University, Center for Economic Research.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
    9. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
    10. Sonja Brangewitz & Jan-Philip Gamp, 2011. "Competitive Outcomes and the Inner Core of NTU Market Games," Working Papers 449, Bielefeld University, Center for Mathematical Economics.
    11. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
    12. Sonja Brangewitz & Jan-Philip Gamp, 2011. "Competitive Outcomes and the Core of TU Market Games," Working Papers 454, Bielefeld University, Center for Mathematical Economics.
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