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


  • Koji Takamiya


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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  • Koji Takamiya, 2006. "Consistency and Unanimity in the House Allocation Problems I: Collective Initial Endowments," ISER Discussion Paper 0657, Institute of Social and Economic Research, Osaka University.
  • Handle: RePEc:dpr:wpaper:0657

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    References listed on IDEAS

    1. Lars Ehlers & Bettina Klaus, 2007. "Consistent House Allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 561-574, March.
    2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    3. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    4. Peleg, Bezalel & Potters, Jos A M & Tijs, Stef H, 1996. "Minimality of Consistent Solutions for Strategic Games, in Particular for Potential Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 81-93, January.
    5. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    6. 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.
    7. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    8. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
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