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Top Trading Cycles with Indifferences under Matroid Constraints

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  • Yasushi Kawase

Abstract

We study the reallocation of indivisible objects among agents who may hold initial endowments and may be indifferent between objects. Each agent has her own set of admissible objects, and a matroid constraint specifies which combinations of assigned objects are feasible. The model contains the housing market, house allocation with newcomers who hold no endowment, and the assignment of students to schools under matroidal constraints at each school. For this model, we introduce the top-class trading cycles mechanism (TCTC), which extends the top trading cycles mechanism (TTC) to matroid constraints and weak preferences. When a trading cycle is selected, TCTC fixes each agent's top indifference class rather than a specific object and postpones the choice within the class to the end. TCTC is individually rational, Pareto efficient, and weakly group-strategy-proof on the full domain of weak preferences, and it runs in polynomial time. When preferences and reports are strict, TCTC is strongly group-strategy-proof. Together with a known impossibility result, our theorem establishes a maximal domain of school-by-school constraints for individual rationality, Pareto efficiency, and strategy-proofness.

Suggested Citation

  • Yasushi Kawase, 2026. "Top Trading Cycles with Indifferences under Matroid Constraints," Papers 2609.32337, arXiv.org.
    • Handle: RePEc:arx:papers:2609.32337
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    References listed on IDEAS

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    1. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
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    3. Julien Combe & Olivier Tercieux & Camille Terrier, 2022. "The Design of Teacher Assignment: Theory and Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3154-3222.
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    6. Imamura, Kenzo & Kawase, Yasushi, 2025. "Efficient and strategy-proof mechanism under general constraints," Theoretical Economics, Econometric Society, vol. 20(2), May.
    7. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
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