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The proportional distribution in a cooperative model with external opportunities

Author

Listed:
  • Camilla Di Luca (Universita degli Studi G. D'Annunzio di Chieti-Pescara)
  • Josep M Izquierdo (Universitat de Barcelona)
  • Carles Rafels (Universitat de Barcelona)

    (Universitat de Barcelona)

Abstract

We study a cooperative problem where agents contribute a certain amount of money or capital in order to obtain a surplus. The proportional distribution with respect to the contributions of players is a core element of the cooperative game associated. Within this basic model, an external agent is introduced in order to evaluate the potential profit of every subcoalition of agents in the case this new agent enters. This analysis can produce that the relative bargaining power of agents may be modified. In particular, we evaluate whether the proportional distribution is still a robust proposal from the point of view of the bargaining set of a cooperative game with coalition structure (Davis and Maschler, 1963). Since, in general, the proportional distribution fails to be a bargaining set element of this game, a sufficient condition for the proportional allocation to belong to the bargaining is stated. A necessary condition is also analysed. Finally, we state a sufficient condition that guarantees the proportional distribution to be the unique element of the bargaining set of the associated game with coalition structure.

Suggested Citation

  • Camilla Di Luca (Universita degli Studi G. D'Annunzio di Chieti-Pescara) & Josep M Izquierdo (Universitat de Barcelona) & Carles Rafels (Universitat de Barcelona), 2011. "The proportional distribution in a cooperative model with external opportunities," Working Papers in Economics 262, Universitat de Barcelona. Espai de Recerca en Economia.
  • Handle: RePEc:bar:bedcje:2011262
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    References listed on IDEAS

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    1. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    2. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(01), pages 17-40, April.
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    JEL classification:

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

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