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The Proportional Value of a Cooperative Game

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  • Barry Feldman

    (Ibbotson Associates)

Abstract

The proportional value is the unique strictly consistent TU and NTU value which, in two-player TU games, gives players equal proportional gains from cooperation. Strict consistency means consistency with respect to the Hart and Mas-Colell (1989) reduced game. The proportional value is a nonlinear analog of the Shapley (1953) value in TU games and the egalitarian value (Kalai and Samet (1985)) in NTU games. It is derived from a ratio potential similar to the Hart and Mas-Colell (1989) diference potential. The propor- tional value is monotonic and is in the core of a log-convex game. It is also the unique equilibrium payoff configuration in a variation of the noncooperative bargaining game of Hart and Mas-Colell (1996) where players' probabilities of participation at any point in the game are proportional to their expected payoff at that time. Thus, it is a model of endogenous power in cooperative games. Application to cost allocation problems is considered.

Suggested Citation

  • Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1140
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    Citations

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    Cited by:

    1. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    2. Rene van den Brink & Rene Levinsky & Miroslav Zeleny, 2007. "The balanced solution for cooperative transferable utility games," Jena Economics Research Papers 2007-073, Friedrich-Schiller-University Jena.
    3. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    4. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    5. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
    6. Besner, Manfred, 2019. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi payoff," MPRA Paper 92247, University Library of Munich, Germany.
    7. Sergei Pechersky, 2001. "On Proportional Excess for NTU Games," EUSP Department of Economics Working Paper Series 2001/02, European University at St. Petersburg, Department of Economics, revised 30 Oct 2001.
    8. Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.
    9. Barry Feldman, 2002. "A Dual Model of Cooperative Value," Game Theory and Information 0207001, University Library of Munich, Germany.

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