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

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  • Koji Takamiya
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    Abstract

    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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    Bibliographic Info

    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. Peleg, B. & Potters, J.A.M. & Tijs, S.H., 1996. "Minimality of consistent solutions for strategic games, in particular for potential games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72912, Tilburg University.
    3. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer, vol. 15(4), pages 257-291, December.
    4. Ehlers,Lars & Klaus,Bettina, 2005. "Consistent House Allocation," Research Memorandum 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. Peleg, B. & Tijs, S.H., 1993. "The consistency principle for games in strategic form," Discussion Paper 1993-6, Tilburg University, Center for Economic Research.
    6. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
    7. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    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.
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