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Population monotonic allocation schemes on externality games

Author

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  • F. Grafe
  • E. Iñarra
  • J. M. Zarzuelo

Abstract

This paper introduces a new class of cooperative games called externality games. In these games each player contributes with their specific endowment and also with their presence to the total worth of the coalition she belongs to. We prove that for these games there exists a unique efficient, anonymous and population monotonic rule: the proportional rule. A subclass of externality games is also analyzed. Games in this subclass are not necessarily convex although we show that the Shapley value is in the core of these games, but it is not a population monotonic rule. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • F. Grafe & E. Iñarra & J. M. Zarzuelo, 1998. "Population monotonic allocation schemes on externality games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 71-80, September.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:1:p:71-80
    DOI: 10.1007/s001860050012
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    Citations

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    Cited by:

    1. Paula Corcho & José Ferreira, 2003. "Generalized externality games," Theory and Decision, Springer, vol. 54(2), pages 163-184, March.
    2. J. Zambujal-Oliveira, 2021. "Supply Chain Innovation Research: A Conceptual Approach of Information Management with Game Theory," Group Decision and Negotiation, Springer, vol. 30(2), pages 377-394, April.
    3. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    4. Takaaki Abe, 2020. "Population monotonic allocation schemes for games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 97-117, March.
    5. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2008. "Production-inventory games and PMAS-games: Characterizations of the Owen point," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 96-108, July.
    6. Josep Maria Izquierdo Aznar, 2003. "Regular Population Monotonic Allocation Schemes and the Core," Working Papers in Economics 110, Universitat de Barcelona. Espai de Recerca en Economia.

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