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A note on object allocation under lexicographic preferences

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  • Saban, Daniela
  • Sethuraman, Jay

Abstract

We consider the problem of allocating m objects to n agents. Each agent has unit demand, and has strict preferences over the objects. There are qj units of object j available and the problem is balanced in the sense that ∑jqj=n. An allocation specifies the amount of each object j that is assigned to each agent i, when the objects are divisible; when the objects are indivisible and exactly one unit of each object is available, an allocation is interpreted as the probability that agent i is assigned one unit of object j. In our setting, agent preferences over objects are extended to preferences over allocations using the natural lexicographic order. The goal is to design mechanisms that are efficient, envy-free, and strategy-proof. Schulman and Vazirani show that an adaptation of the probabilistic serial mechanism satisfies all these properties when qj≥1 for all objects j. Our first main result is a characterization of problems for which efficiency, envy-freeness, and strategy-proofness are compatible. Furthermore, we show that these three properties do not characterize the serial mechanism. Finally, we show that when indifferences between objects are permitted in agent preferences, it is impossible to satisfy all three properties even in the standard setting of “house” allocation in which all object supplies are 1.

Suggested Citation

  • Saban, Daniela & Sethuraman, Jay, 2014. "A note on object allocation under lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 283-289.
  • Handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:283-289
    DOI: 10.1016/j.jmateco.2013.12.002
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    References listed on IDEAS

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    1. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    2. 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.
    3. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    4. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
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    Cited by:

    1. Katarina Cechlarova & Bettina Klaus & David F.Manlove, 2016. "Pareto optimal matchings of students to courses in the presence of prerequisites," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 16.04, Université de Lausanne, Faculté des HEC, DEEP.
    2. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    3. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    4. Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.

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