Upper-contour strategy-proofness in the probabilistic assignment problem

  • Youngsub ChunEmail author
  • Kiyong Yun
Original Paper


Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001) show that there is no rule satisfying stochastic dominance efficiency,equal treatment of equals and stochastic dominance strategy-proofness for a probabilistic assignment problem of indivisible objects. Recently, Mennle and Seuken (Partial strategyproofness: relaxing strategy-proofness for the random assignment problem. Mimeo, 2017) show that stochastic dominance strategy-proofness is equivalent to the combination of three axioms, swap monotonicity,upper invariance, and lower invariance. In this paper, we introduce a weakening of stochastic dominance strategy-proofness, called upper-contour strategy-proofness, which requires that if the upper-contour sets of some objects are the same in two preference relations, then the sum of probabilities assigned to the objects in the two upper-contour sets should be the same. First, we show that upper-contour strategy-proofness is equivalent to the combination of two axioms, upper invariance and lower invariance. Next, we show that the impossibility result still holds even though stochastic dominance strategy-proofness is weakened to upper-contour strategy-proofness.



  1. Bogomolnaia A, Heo EJ (2012) Probabilistic assignment of objects: characterizing the serial rule. J Econ Theory 147:2072–2082CrossRefGoogle Scholar
  2. Bogomolnaia A, Moulin H (2001) A new solution to the random assignment problem. J Econ Theory 100:295–328CrossRefGoogle Scholar
  3. Bogomolnaia A, Moulin H (2002) A simple random assignment problem with a unique solution. Econ Theor 19:623–635CrossRefGoogle Scholar
  4. Carroll G (2012) When are local incentive constraints sufficient? Econometrica 80(2):661–686CrossRefGoogle Scholar
  5. Chang H, Chun Y (2017) Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object. Math Soc Sci 90:80–92CrossRefGoogle Scholar
  6. Cho WJ (2016) Incentive properties for ordinal mechanisms. Games Econ Behav 95:168–177CrossRefGoogle Scholar
  7. Hashimoto T, Hirata D, Kesten O, Kurino M, Unver U (2014) Two axiomatic approaches to the probabilistic serial mechanism. Theor Econ 9:253–277CrossRefGoogle Scholar
  8. Heo EJ (2014) Probabilistic assignment problem with multi-unit demands: a generalization of the serial rule and its characterization. J Math Econ 54:40–47CrossRefGoogle Scholar
  9. Heo EJ, Yılmaz Ö (2015) A characterization of the extended serial correspondence. J Math Econ 59:102–110CrossRefGoogle Scholar
  10. Hylland A, Zeckhauser R (1979) The efficient allocation of individuals to positions. J Political Econ 87:293–314CrossRefGoogle Scholar
  11. Kasajima Y (2013) Probabilistic assignment of indivisible goods with single-peaked preferences. Soc Choice Welf 41:203–215CrossRefGoogle Scholar
  12. Liu P, Zeng H (2019) Random assignment on preference domains with a tier structure. J Math Econ 84:176–194CrossRefGoogle Scholar
  13. Mennle T, Seuken S (2017) Partial strategyproofness: relaxing strategy-proofness for the random assignment problem. MimeoGoogle Scholar
  14. Nesterov A (2017) Fairness and efficiency in strategy-proof object allocation mechanisms. J Econ Theory 170:145–168CrossRefGoogle Scholar
  15. Sato S (2013) A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one. J Econ Theory 148(1):259–278CrossRefGoogle Scholar
  16. Zhou L (1990) On a conjecture by Gale about one-sided matching problems. J Econ Theory 52:123–135CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of EconomicsSeoul National UniversitySeoulSouth Korea

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