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The Banzhaf Value in the Presence of Externalities

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  • Mikel Álvarez-Mozos

    ()
    (Facultat d'Economia i Empresa; Universitat de Barcelona (UB))

  • Oriol Tejada Pinyol

    ()
    (CER-ETH, ETH Zurich)

Abstract

We propose two generalizations of the Banzhaf value for partition function form games. In both cases, our approach is based on probability distributions over the set of possible coalition structures that may arise for any given set of agents. First, we introduce a family of values, one for each collection of the latter probability distributions, defined as the Banzhaf value of an expected coalitional game. Then, we provide two characterization results for this new family of values within the framework of all partition function games. Both results rely on a property of neutrality with respect to am algamation of players. Second, as this collusion transformation fails to be meanin gful for simple games in partition function form, we propose another generalization of the Banzhaf value which also builds on probability distributions of the above type. This latter family is characterized by means of a neutrality property which uses an amalgamation transformation of players for which simple games are close

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Bibliographic Info

Paper provided by Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics in its series UB Economics Working Papers with number 2014/302.

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Length: 20 pages
Date of creation: 2014
Date of revision:
Handle: RePEc:ewp:wpaper:302web

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Keywords: Banzhaf value; Externalities; Games in partition function form; Simplegames.;

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  1. 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.
  2. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  3. Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
  4. 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.
  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. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
  7. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  8. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
  9. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer, vol. 26(1), pages 137-141.
  10. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
  11. André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer, vol. 41(3), pages 497-515, August.
  12. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
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