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Consistency and Unanimity in the House Allocation Problems I: Collective Initial Endowments

  • Koji Takamiya
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    This paper studies allocation correspondences in the house allocation problems with collective initial endowments. We examine the implications of two axioms, namely "consistency" and "unanimity." Consistency requires the allocation correspondence be invariant under reductions of population. Unanimity requires the allocation correspondence respect unanimity, that is, it assigns to every agent the object that ranks best for him whenever possible. We prove that if an allocation correspondence satisfies these two axioms, then it is a subcorrespondence of the Pareto correspondence. Further, we give a characterization of the Pareto correspondence using a version of "converse consistency."

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    File URL: http://www.iser.osaka-u.ac.jp/library/dp/2006/DP0657.pdf
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    Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0657.

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    Date of creation: Mar 2006
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    Handle: RePEc:dpr:wpaper:0657
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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. EHLERS, Lars & KLAUS, Bettina, 2005. "Consistent House Allocation," Cahiers de recherche 2005-08, Universite de Montreal, Departement de sciences economiques.
    3. Peleg, B. & Tijs, S., 1993. "The Consistency Principle for Games in Strategic Form," Papers 9306, Tilburg - Center for Economic Research.
    4. repec:ner:tilbur:urn:nbn:nl:ui:12-72911 is not listed on IDEAS
    5. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
    6. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer, vol. 15(4), pages 257-291, December.
    7. Peleg, B. & Potters, J.A.M. & Tijs, S.H., 1996. "Minimality of consistent solutions for strategic games, in particular for potential games," Other publications TiSEM 159e2ef3-4411-4900-9bf1-b, Tilburg University, School of Economics and Management.
    8. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    9. repec:ner:tilbur:urn:nbn:nl:ui:12-72912 is not listed on IDEAS
    10. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
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