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A Dual Description of the Class of Games with a Population Monotonic Allocation Scheme


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  • Norde, H.W.
  • Reijnierse, J.H.

    (Tilburg University, Center for Economic Research)


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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-99.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:200099

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Keywords: game theory;

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  1. Moulin, H, 1990. "Cores and Large Cores When Population Varies," International Journal of Game Theory, Springer, vol. 19(2), pages 219-32.
  2. 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. 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, vol. 18(2), pages 493-508, December.
  2. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M., 2006. "Population Monotonic Path Schemes for Simple Games," Discussion Paper 2006-113, Tilburg University, Center for Economic Research.
  3. Slikker, M. & Norde, H.W., 2008. "The Monoclus of a Coalitional Game," Discussion Paper 2008-6, Tilburg University, Center for Economic Research.
  4. 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.
  5. 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.


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