A note on object allocation under lexicographic preferences
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.
Volume (Year): 50 (2014)
Issue (Month): C ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/jmateco|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:50:y:2014:i:c:p:283-289. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.