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Stability, Strategy-Proofness, and Cumulative Offer Mechanisms
[Stability and Incentives for College Admissions with Budget Constraints]

Author

Listed:
  • John William Hatfield
  • Scott Duke Kominers
  • Alexander Westkamp

Abstract

We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulability via contractual terms—and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: if the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice.

Suggested Citation

  • John William Hatfield & Scott Duke Kominers & Alexander Westkamp, 2021. "Stability, Strategy-Proofness, and Cumulative Offer Mechanisms [Stability and Incentives for College Admissions with Budget Constraints]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1457-1502.
    • Handle: RePEc:oup:restud:v:88:y:2021:i:3:p:1457-1502.
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    File URL: http://hdl.handle.net/10.1093/restud/rdaa052
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    Citations

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    Cited by:

    1. Zhou, Yu & Serizawa, Shigehiro, 2023. "Multi-object auction design beyond quasi-linearity: Leading examples," Games and Economic Behavior, Elsevier, vol. 140(C), pages 210-228.
    2. Mackenzie, Andrew & Zhou, Yu, 2022. "Menu mechanisms," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Zhang, Jun, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    4. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    5. 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).
    6. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2021. "Redesigning the US Army’s Branching Process: A Case Study in Minimalist Market Design," NBER Working Papers 28911, National Bureau of Economic Research, Inc.
    7. Yu Zhou & Shigehiro Serizawa, 2021. "Multi-object Auction Design Beyond Quasi-linearity: Leading Examples," ISER Discussion Paper 1116r, Institute of Social and Economic Research, Osaka University, revised Nov 2022.
    8. Yi-You Yang, 2023. "Firm-quasi-stability and re-equilibration in matching markets with contracts," Papers 2305.17948, arXiv.org, revised Jul 2023.
    9. Bando, Keisuke & Hirai, Toshiyuki & Zhang, Jun, 2021. "Substitutes and stability for many-to-many matching with contracts," Games and Economic Behavior, Elsevier, vol. 129(C), pages 503-512.
    10. Tsuyoshi Adachi & Yuki Ishibashi, 2022. "Stability and strategy-proofness for matching with interval constraints," Working Papers 2124, Waseda University, Faculty of Political Science and Economics.
    11. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.

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