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Dividends and weighted values in games with externalities

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  • Inés Macho-Stadler

    ()

  • David Pérez-Castrillo

    ()

  • David Wettstein

    ()

Abstract

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 39 (2010)
Issue (Month): 1 (March)
Pages: 177-184

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Handle: RePEc:spr:jogath:v:39:y:2010:i:1:p:177-184

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Related research

Keywords: Games with externalities; Sharing rules; Dividends; D62; C71;

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References

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  1. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008. "Dividends and Weighted Values in Games with Externalities," UFAE and IAE Working Papers 758.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Kim Hang Pham Do & Henk Norde, 2007. "The Shapley Value For Partition Function Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 353-360.
  3. Guillaume Haeringer, 1998. "A new weight scheme for the Shapley value," Game Theory and Information 9807001, EconWPA.
  4. McQuillin, Ben, 2009. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," Journal of Economic Theory, Elsevier, vol. 144(2), pages 696-721, March.
  5. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
  6. Inés Macho & David Pérez-Castrillo & David Wettstein, 2005. "Efficient Bidding with Externalitites," Working Papers 159, Barcelona Graduate School of Economics.
  7. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2004. "Sharing the surplus: A just and efficient proposal for environments with externalities," UFAE and IAE Working Papers 611.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  8. Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008. "Externalities, Potential, Value And Consistency," Working papers 168, Centre for Development Economics, Delhi School of Economics.
  9. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
  10. Perez-Castrillo, D. & Wettstein, D., 1999. "Bidding for the Surplus: a Non-Cooperative Approach to the Shapley Value. ation," Papers 24-99, Tel Aviv.
  11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  12. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
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Cited by:
  1. 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.
  2. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer, vol. 39(1), pages 177-184, March.

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