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A dual description of the class of games with a population monotonic allocation scheme

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  • Norde, Henk
  • Reijnierse, Hans

Abstract

A vector of balanced weights infers an inequality that games with a nonempty core obey.This paper gives a generalization of the notion `vector of balanced weights'.Herewith it provides necessary and sufficient conditions to determine whether a TU-game has a population monotonic allocation scheme or not. Furthermore it shows that every 4-person integer valued game with a population monotonic allocation scheme has an integer valued population monotonic allocation scheme and it gives an example of a 7-person integer valued game that has only non-integer valued population monotonic allocation schemes.
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Suggested Citation

  • Norde, Henk & Reijnierse, Hans, 2002. "A dual description of the class of games with a population monotonic allocation scheme," Games and Economic Behavior, Elsevier, vol. 41(2), pages 322-343, November.
    • Handle: RePEc:eee:gamebe:v:41:y:2002:i:2:p:322-343
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    References listed on IDEAS

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    1. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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    Cited by:

    1. Josep M. Izquierdo & Jesús Montes & Carlos Rafels, 2024. "Population Lorenz-monotonic allocation schemes for TU-games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 417-436, September.
    2. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    3. Bas Dietzenbacher & Emre Doğan, 2025. "Population monotonicity and egalitarianism," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-18, December.
    4. Jesús Getán & Jesús Montes, 2010. "On cooperative games with large monotonic core," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 493-508, December.
    5. Slikker, Marco & Norde, Henk, 2011. "The monoclus of a coalitional game," Games and Economic Behavior, Elsevier, vol. 71(2), pages 420-435, March.
    6. Loe Schlicher & Marco Slikker & Willem van Jaarsveld & Geert-Jan van Houtum, 2020. "Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1445-1465, November.
    7. Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    8. Tamás Solymosi, 2024. "Assignment games with population monotonic allocation schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 67-88, February.
    9. Jesus Fco. Getan Olivan & Jesus Montes & Carlos Rafels Pallarola, 2006. "On the monotonic core," Working Papers in Economics 155, Universitat de Barcelona. Espai de Recerca en Economia.
    10. Slikker, M. & Norde, H.W., 2008. "The Monoclus of a Coalitional Game," Other publications TiSEM 8b2bae34-674a-4632-a64e-9, Tilburg University, School of Economics and Management.
    11. Jesus Getan & Jesus Montes, 2008. "A characterization of cooperative TU-games with large monotonic core," Working Papers in Economics 193, Universitat de Barcelona. Espai de Recerca en Economia.

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