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Comment on “Assignment problems with complementarities” [J. Econ. Theory 165 (2016) 209-241]

Author

Listed:
  • Kornbluth, Daniel
  • Kushnir, Alexey
  • Nguyen, Thanh
  • Vohra, Rakesh

Abstract

Nguyen et al. (2016) introduce the Bundled Probabilistic Serial and Bundled Probabilistic Serial under Limited Complementarities mechanisms for allocating bundles of indivisible objects under ordinal preferences over bundles. They present efficiency, fairness, and incentive properties of the two mechanisms, showing both to be ordinally efficient, weakly envy-free, weakly strategy-proof, and asymptotically strategy-proof. We provide counterexamples demonstrating that the Bundled Probabilistic Serial mechanism is not weakly strategy-proof and the Bundled Probabilistic Serial under Limited Complementarities mechanism is not weakly envy-free, weakly strategy-proof, or asymptotically strategy-proof. We also revise proofs for the remaining properties.

Suggested Citation

  • Kornbluth, Daniel & Kushnir, Alexey & Nguyen, Thanh & Vohra, Rakesh, 2026. "Comment on “Assignment problems with complementarities” [J. Econ. Theory 165 (2016) 209-241]," Journal of Economic Theory, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:jetheo:v:231:y:2026:i:c:s0022053125001760
    DOI: 10.1016/j.jet.2025.106130
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    References listed on IDEAS

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    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
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    4. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    5. Martin Bichler & Soeren Merting, 2021. "Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3540-3559, October.
    6. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
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    8. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    9. Daniel Kornbluth & Alexey Kushnir, 2024. "Undergraduate Course Allocation through Competitive Markets," Papers 2412.05691, arXiv.org, revised Dec 2025.
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    Keywords

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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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