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A new weight scheme for the Shapley value

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  • Haeringer, Guillaume

Abstract

It is well known since Owen (Management Science, 1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e. of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be interpreted as a measure of bargaining power. Two different axiomatic characterization of this new value are proposed: one including the weights in the axioms and one without.
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Suggested Citation

  • Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
  • Handle: RePEc:eee:matsoc:v:52:y:2006:i:1:p:88-98
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    References listed on IDEAS

    as
    1. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    Cited by:

    1. repec:hal:journl:halshs-00881125 is not listed on IDEAS
    2. Amandine Ghintran, 2008. "A weighted position value," Post-Print hal-00332573, HAL.
    3. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    4. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    5. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
    6. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01207823, HAL.
    7. repec:hal:journl:halshs-01207823 is not listed on IDEAS
    8. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 177-184, March.
    9. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    10. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications, Elsevier.
    11. Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "An axiomatic approach to composite solutions," Center for Mathematical Economics Working Papers 385, Center for Mathematical Economics, Bielefeld University.
    12. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    13. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1074-4 is not listed on IDEAS
    14. Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2016. "The proportional Shapley value and an application," Working Papers hal-01362228, HAL.
    15. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    16. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.
    17. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
    18. Wilson da C. Vieira, 2015. "Allocation of costs to clean up a polluted river: an axiomatic approach," Economics Bulletin, AccessEcon, vol. 35(2), pages 1216-1226.
    19. repec:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500128 is not listed on IDEAS
    20. 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.
    21. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01207823, HAL.

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    JEL classification:

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

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