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Pyramidal values

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  • Ramón Flores
  • Elisenda Molina
  • Juan Tejada

Abstract

We propose and analyze a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary, and the rest of his marginal contribution to the just formed coalition is distributed among the incumbent players. We relate the pyramidal-type sharing scheme we propose with other sharing schemes, and we also obtain some known values by means of this kind of pyramidal procedures. In particular, we show that the Shapley value can be obtained by means of an interesting pyramidal procedure that distributes nonzero dividends among the incumbents. As a result, we obtain an alternative formulation of the Shapley value based on a measure of complementarity between two players. Finally, we introduce the family of proportional pyramidal values, in which an incumbent receives a dividend in proportion to his initial investment, measured by means of his marginal contribution. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Ramón Flores & Elisenda Molina & Juan Tejada, 2014. "Pyramidal values," Annals of Operations Research, Springer, vol. 217(1), pages 233-252, June.
    • Handle: RePEc:spr:annopr:v:217:y:2014:i:1:p:233-252:10.1007/s10479-013-1509-y
    DOI: 10.1007/s10479-013-1509-y
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    References listed on IDEAS

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    Cited by:

    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.

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