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On Harsanyi Payoff Vectors and the Weber Set

Author

Listed:
  • Jean Derks

    (Universiteit Maastricht)

  • Gerard van der Laan

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Valeri Vasil'ev

    (Sobolev Institute of Mathematics, Russia)

Abstract

The paper discusses the set of Harsanyi payoff vectors,also known as the Selectope. First, we reconsider some results on Harsanyi payoff vectors, published by Vasil'ev in the late 1970's, within a more general framework. In particular, these results state already that the set of Harsanyi payoff vectors is given by the core of an associated convex game, a result that recently has been proven by Derks et. al.(2000). The marginal contribution vectors are examples of Harsanyi payoff vectors so that the Weber set, being the convex hull of the marginal contribution vectors, is a subset of the Harsanyi set, which denotes the set of Harsanyi payoff vectors. We provide two characterizations of those Harsanyi payoff vectors that are elements of the Weber set.

Suggested Citation

  • Jean Derks & Gerard van der Laan & Valeri Vasil'ev, 2002. "On Harsanyi Payoff Vectors and the Weber Set," Tinbergen Institute Discussion Papers 02-105/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20020105
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    File URL: https://papers.tinbergen.nl/02105.pdf
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    Citations

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    Cited by:

    1. Valeri Vasil'Ev, 2007. "Weber Polyhedron And Weighted Shapley Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 139-150.
    2. Derks, Jean, 2005. "A new proof for Weber's characterization of the random order values," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 327-334, May.

    More about this item

    Keywords

    TU-games; Core; Harsanyi set; Weber set; Selectope.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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