TY - JOUR
T1 - Probabilistic assignment
T2 - an extension approach
AU - Cho, Wonki Jo
N1 - Funding Information:
I am grateful to William Thomson for his inspiration, encouragement, and support. I thank an Associate Editor and an anonymous referee for comments that greatly improved the earlier version of this paper. I also thank Paulo Barelli, Srihari Govindan, Biung-Ghi Ju, Hervé Moulin, Romans Pancs, Jay Sethuraman, and seminar participants at Korea University, Seoul National University, UC Riverside, Hitotsubashi University, Sogang University, the 2011 Society for Economic Design Conference, and the 23rd International Conference on Game Theory for their comments. This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2016S1A3A2924944).
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We study the problem of allocating objects using lotteries when agents only submit preferences over objects. A standard approach is to “extend” agents’ preferences over objects to preferences over lotteries, using (first-order) stochastic dominance, or the sd-extension. Following (Cho, Games Econ Behav 95:168–177, 2016a), we complement this approach with two alternative extensions, the dl- and ul- extensions, that give rise to lexicographic preferences (dl stands for “downward lexicographic” and ul for “upward lexicographic”) and apply all three of them in tandem to probabilistic assignment. Each property of rules now has three versions that vary with the extension chosen. We introduce a family of rules that generalizes the probabilistic serial rule. Then we study their behavior, as well as that of the random priority rule, in terms of efficiency, no-envy, and strategy-proofness.
AB - We study the problem of allocating objects using lotteries when agents only submit preferences over objects. A standard approach is to “extend” agents’ preferences over objects to preferences over lotteries, using (first-order) stochastic dominance, or the sd-extension. Following (Cho, Games Econ Behav 95:168–177, 2016a), we complement this approach with two alternative extensions, the dl- and ul- extensions, that give rise to lexicographic preferences (dl stands for “downward lexicographic” and ul for “upward lexicographic”) and apply all three of them in tandem to probabilistic assignment. Each property of rules now has three versions that vary with the extension chosen. We introduce a family of rules that generalizes the probabilistic serial rule. Then we study their behavior, as well as that of the random priority rule, in terms of efficiency, no-envy, and strategy-proofness.
UR - http://www.scopus.com/inward/record.url?scp=85040929376&partnerID=8YFLogxK
U2 - 10.1007/s00355-018-1110-z
DO - 10.1007/s00355-018-1110-z
M3 - Article
AN - SCOPUS:85040929376
SN - 0176-1714
VL - 51
SP - 137
EP - 162
JO - Social Choice and Welfare
JF - Social Choice and Welfare
IS - 1
ER -