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Assignment problems with complementarities

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  • Nguyen, Thành
  • Peivandi, Ahmad
  • Vohra, Rakesh

Abstract

The problem of allocating bundles of indivisible objects without transfers arises in many practical settings, including the assignment of courses to students, of siblings to schools, and of truckloads of food to food banks. In these settings, the complementarities in preferences are small compared with the size of the market. We exploit this to design mechanisms satisfying constrained efficiency and asymptotic strategy-proofness. We introduce two mechanisms, one for cardinal and the other for ordinal preferences. When agents do not want bundles of size larger than k, these mechanisms over-allocate each good by at most k−1 units, ex-post. These results are based on a generalization of the Birkhoff–von Neumann theorem on how probability shares of bundles can be expressed as lotteries over approximately feasible allocations, which is of independent interest.

Suggested Citation

  • Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
  • Handle: RePEc:eee:jetheo:v:165:y:2016:i:c:p:209-241
    DOI: 10.1016/j.jet.2016.04.006
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    Cited by:

    1. Daniel Kornbluth & Alexey Kushnir, 2024. "Undergraduate Course Allocation through Competitive Markets," Papers 2412.05691, arXiv.org.
    2. Julien Combe & Vladyslav Nora & Olivier Tercieux, 2021. "Dynamic assignment without money: Optimality of spot mechanisms," Working Papers 2021-11, Center for Research in Economics and Statistics.
    3. Karaenke, Paul & Bichler, Martin & Merting, Soeren & Minner, Stefan, 2020. "Non-monetary coordination mechanisms for time slot allocation in warehouse delivery," European Journal of Operational Research, Elsevier, vol. 286(3), pages 897-907.
    4. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    5. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    6. Hashimoto, Tadashi, 2018. "The generalized random priority mechanism with budgets," Journal of Economic Theory, Elsevier, vol. 177(C), pages 708-733.
    7. Hai Nguyen & Thành Nguyen & Alexander Teytelboym, 2021. "Stability in Matching Markets with Complex Constraints," Management Science, INFORMS, vol. 67(12), pages 7438-7454, December.
    8. Honda, Edward, 2021. "A modified deferred acceptance algorithm for conditionally lexicographic-substitutable preferences," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    9. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    10. Eirinakis, Pavlos & Mourtos, Ioannis & Zampou, Eleni, 2022. "Random Serial Dictatorship for horizontal collaboration in logistics," Omega, Elsevier, vol. 111(C).
    11. Alon Eden & Michal Feldman & Ophir Friedler & Inbal Talgam-Cohen & S. Matthew Weinberg, 2021. "A Simple and Approximately Optimal Mechanism for a Buyer with Complements," Operations Research, INFORMS, vol. 69(1), pages 188-206, January.
    12. Martin Bichler & Alexander Hammerl & Thayer Morrill & Stefan Waldherr, 2021. "How to Assign Scarce Resources Without Money: Designing Information Systems that are Efficient, Truthful, and (Pretty) Fair," Information Systems Research, INFORMS, vol. 32(2), pages 335-355, June.
    13. Eric Budish & Judd B. Kessler, 2022. "Can Market Participants Report Their Preferences Accurately (Enough)?," Management Science, INFORMS, vol. 68(2), pages 1107-1130, February.
    14. Priyanka Shende, 2020. "Constrained Serial Rule on the Full Preference Domain," Papers 2011.01178, arXiv.org.
    15. Ata Atay & Antonio Romero-Medina, 2023. "Complementarities in childcare allocation under priorities," Papers 2308.14689, arXiv.org.
    16. Xepapadeas, Petros, 2023. "Multi-agent, multi-site resource allocation under quotas with a Stackelberg leader and network externalities," Economic Modelling, Elsevier, vol. 121(C).
    17. Kevin Riehl & Anastasios Kouvelas & Michail Makridis, 2024. "Fair Money -- Public Good Value Pricing With Karma Economies," Papers 2407.05132, arXiv.org.
    18. 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.
    19. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.

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    More about this item

    Keywords

    One sided matching; Complementarities; Strategy-proof; Efficient; Envy-free; Mechanism;
    All these keywords.

    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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