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On endowments and indivisibility: partial ownership in the Shapley–Scarf model

Author

Listed:
  • Patrick Harless

    (University of Arizona)

  • William Phan

    (North Carolina State University)

Abstract

We introduce a parameterized measure of partial ownership, the $$\alpha $$ α -endowment lower bound, appropriate to probabilistic allocation. Strikingly, among all convex combinations of efficient and group strategy-proof rules, only Gale’s Top Trading Cycles is sd efficient and meets a positive $$\alpha $$ α -endowment lower bound (Theorem 2); for efficiency, partial ownership must in fact be complete. We also characterize the rules meeting each $$\alpha $$ α -endowment lower bound (Theorem 1). For each bound, the family is a semilattice ordered by strength of ownership rights. It includes rules where agents’ partial ownership lower bounds are met exactly, rules conferring stronger ownership rights, and the full endowments of TTC. This illustrates the trade-off between sd efficiency and flexible choice of ownership rights.

Suggested Citation

  • Patrick Harless & William Phan, 2020. "On endowments and indivisibility: partial ownership in the Shapley–Scarf model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 411-435, September.
    • Handle: RePEc:spr:joecth:v:70:y:2020:i:2:d:10.1007_s00199-019-01213-8
    DOI: 10.1007/s00199-019-01213-8
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    Cited by:

    1. Bettina Klaus & Claudia Meo, 2023. "The core for housing markets with limited externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 779-811, October.
    2. Yan Long, 2024. "Achieving the maximum size for exchange problems with dichotomous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 649-669, September.
    3. Harless, Patrick & Phan, William, 2022. "Efficient mixtures of priority rules for assigning objects," Games and Economic Behavior, Elsevier, vol. 132(C), pages 73-89.

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    More about this item

    Keywords

    Object reallocation; Top trading cycles; $$alpha $$ α -endowment;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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