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Weber Polyhedron And Weighted Shapley Values

Author

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  • VALERI VASIL'EV

    (Sobolev Institute of Mathematics, Prosp. Koptyuga 4, 630090 Novosibirsk, Russia)

Abstract

In this paper, we consider the relationship between the Weber set and the Shapley set being the set of all weighted Shapley values of a TU-game. In particular, we propose a new proof for the fact that the Weber set always includes the Shapley set. It is shown that the inclusion mentioned follows directly from the representation theorem for the Weber set, established by Vasil'ev and van der Laan (2002),Siberian Adv. Math., V.12, N2, 97–125. Since the representation theorem applied is formulated in terms of the dividend sharing systems belonging to the so-called Weber polyhedron, we pay strong attention to some monotonicity properties of this polyhedron. Specifically, by making use of induction techniques, a new proof of the strong monotonicity of the Weberd-systems is obtained, and a simplified description of the Weber polyhedron is given.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:01:n:s0219198907001321
    DOI: 10.1142/S0219198907001321
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.

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    More about this item

    Keywords

    Harsanyi set; Weber polyhedron; Weber set; weighted Shapley values; JEL-Code: C71;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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