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Reclaim-proof allocation of indivisible objects

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  • Ekici, Özgün
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    Abstract

    We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.

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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 81 (2013)
    Issue (Month): C ()
    Pages: 1-10

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    Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:1-10
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

    Keywords: Indivisible object allocation; House allocation with existing tenants; House allocation; Housing market; Reclaim-proof; Competitive allocation; Core;

    Find related papers by JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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    1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Game Theory and Information 0408001, EconWPA, revised 16 Feb 2005.
    2. 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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    6. Svensson, Lars-Gunnar & Larsson, Bo, 2002. "Strategy-Proofness, Core, and Sequential Trade," Working Papers 2002:14, Lund University, Department of Economics, revised 09 May 2003.
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    8. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    9. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
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    11. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
    12. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    13. Sönmez, Tayfun & Ünver, M. Utku, 2010. "House allocation with existing tenants: A characterization," Games and Economic Behavior, Elsevier, vol. 69(2), pages 425-445, July.
    14. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer, vol. 23(1), pages 75-83.
    15. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer, vol. 16(4), pages 557-567.
    16. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    17. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    18. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
    19. 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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