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Consistency and Monotonicity in Assignment Problems

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  • Sasaki, Hiroo
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    Abstract

    This paper presents axiomatic characterizations of the core of assignment problems. In the main axiomatization theorem we use six axioms including the consistency (CONS) and the weak pairwise-monotonicity (W.P.MON) which are firstly proposed and defined for this setup in the present paper. Since an assignment problem may be converted into a model of a private ownership economy with indivisible goods and the core of the assignment problems coincides with the set of the competitive allocations of the economy, our characterization theorems also give axiomatic characterizations of the set of competitive allocations. Because the consistency is a desirable property of resource allocation mechanisms, our main result gives a new normative implication of competitive equilibria.

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 24 (1995)
    Issue (Month): 4 ()
    Pages: 373-97

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    Handle: RePEc:spr:jogath:v:24:y:1995:i:4:p:373-97

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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Cited by:
    1. Özen, Ulaş & Erkip, Nesim & Slikker, Marco, 2012. "Stability and monotonicity in newsvendor situations," European Journal of Operational Research, Elsevier, vol. 218(2), pages 416-425.
    2. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer, vol. 15(4), pages 257-291, December.
    3. Llorca, N. & Tijs, S.H. & Timmer, J.B., 1999. "Semi-Infinite Assignment Problems and Related Games," Discussion Paper 1999-74, Tilburg University, Center for Economic Research.
    4. Toda, Manabu, 2005. "Axiomatization of the core of assignment games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 248-261, November.
    5. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    6. Sanchez-Soriano, Joaquin, 2003. "The pairwise egalitarian solution," European Journal of Operational Research, Elsevier, vol. 150(1), pages 220-231, October.
    7. Francesc Llerena (Universitat Rovira i Virgili - CREIP) & Marina Nunez (Universitat de Barcelona) & Carles Rafels (Universitat de Barcelona), 2012. "An axiomatization of the nucleolus of the assignment game," Working Papers in Economics 286, Universitat de Barcelona. Espai de Recerca en Economia.
    8. Borm, P.E.M. & Hamers, H.J.M. & Hendrickx, R.L.P., 2001. "Operations Research Games: A Survey," Discussion Paper 2001-45, Tilburg University, Center for Economic Research.
    9. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée.

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