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On proper Shapley values for monotone TU-games

Author

Listed:
  • René Brink
  • René Levínský

    ()

  • Miroslav Zelený

Abstract

The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. A proper Shapley value, introduced in Vorob’ev and Liapounov (Game Theory and Applications, vol IV. Nova Science, New York, pp 155–159, 1998 ), assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. In this contribution we investigate these proper Shapley values in the context of monotone games. We prove their existence for all monotone transferable utility games and discuss other properties of this solution. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:449-471
    DOI: 10.1007/s00182-014-0439-5
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    References listed on IDEAS

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    Cited by:

    1. Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2016. "The proportional Shapley value and an application," Working Papers hal-01362228, HAL.
    2. Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.

    More about this item

    Keywords

    Proper Shapley value; Proportionality; Weighted Shapley value; Shapley mapping; Fixed point; C71;

    JEL classification:

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

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