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Pyramidal values

Author

Listed:
  • Flores Díaz, Ramón Jesús
  • Molina, Elisenda
  • Tejada, Juan

Abstract

We propose 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 right to get part of the benefits derived from subsequent incorporations to the just formed coalition, whereas the remaining benefit is distributed among the incumbent players. To be specific, we consider some parametric families of pyramidal values: the egalitarian pyramidal family, which coincides with the a-consensus value family introduced by Ju et al. in (2007), the proportional pyramidal family, and the weighted pyramidal family, which in turn includes the other two families as special cases. We also analyze the properties of these families, as well as their relationships with other previously defined values.

Suggested Citation

  • Flores Díaz, Ramón Jesús & Molina, Elisenda & Tejada, Juan, 2012. "Pyramidal values," DES - Working Papers. Statistics and Econometrics. WS ws122418, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws122418
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    References listed on IDEAS

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    1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    2. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
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