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Dividends and Weighted Values in Games with Externalities

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  • Ines Macho-Stadler

    ()
    (Dep. of Economics & CODE, Universitat Autonoma de Barcelona, Spain)

  • David Perez-Castrillo

    ()
    (Dep. of Economics & CODE, Universitat Autonoma de Barcelona,Spain)

  • David Wettstein

    ()
    (Dep. of Economics, Ben-Gurion University of the Negev)

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

Paper provided by Ben-Gurion University of the Negev, Department of Economics in its series Working Papers with number 0906.

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Length: 19 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:bgu:wpaper:0906

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References

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  1. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2006. "Efficient bidding with externalities," Games and Economic Behavior, Elsevier, vol. 57(2), pages 304-320, November.
  2. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
  3. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2004. "Sharing the surplus: A just and efficient proposal for environments with externalities," Working Papers 119, Barcelona Graduate School of Economics.
  4. McQuillin, Ben, 2008. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," MPRA Paper 12049, University Library of Munich, Germany.
  5. Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008. "Externalities, Potential, Value And Consistency," Working papers 168, Centre for Development Economics, Delhi School of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  11. Perez-Castrillo, D. & Wettstein, D., 1999. "Bidding for the Surplus: a Non-Cooperative Approach to the Shapley Value. ation," Papers 24-99, Tel Aviv.
  12. 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.
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Cited by:
  1. 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.
  2. 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.

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