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Sequential decisions in allocation problems

Author

Listed:
  • Josep Maria Izquierdo Aznar
  • Francesc Llerena
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequential decision problem. In each step of the process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentially compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersection of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantageous properties for the first player.

Suggested Citation

  • Josep Maria Izquierdo Aznar & Francesc Llerena & Carlos Rafels Pallarola, 2004. "Sequential decisions in allocation problems," Working Papers in Economics 116, Universitat de Barcelona. Espai de Recerca en Economia.
    • Handle: RePEc:bar:bedcje:2004116
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    References listed on IDEAS

    as
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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