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Top Trading Cycles, Consistency, and Acyclic Priorities for House Allocation with Existing Tenants

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  • Bettina Klaus
  • Jan-Christoph Schlegel
  • Mehmet Karakaya

Abstract

We study the house allocation with existing tenants model (Abdulkadiroglu and Sonmez, 1999) and consider rules that allocate houses based on priorities. We introduce a new acyclicity requirement and show that for house allocation with existing tenants a top trading cycles (TTC) rule is consistent if and only if its underlying priority structure satis es our acyclicity condition. Next we give an alternative description of TTC rules based on ownership-adapted acyclic priorities in terms of two speci c rules,YRMH-IGYT (you request my house - I get your turn) and ecient priority rules,that are applied in two steps. Moreover, even if no priority structure is a priori given,we show that a rule is a top trading cycles rule based on ownership-adapted acyclic priorities if and only if it satis es Pareto-optimality, individual-rationality, strategy-proofness, consistency, and either reallocation-proofness or non-bossiness.

Suggested Citation

  • Bettina Klaus & Jan-Christoph Schlegel & Mehmet Karakaya, 2019. "Top Trading Cycles, Consistency, and Acyclic Priorities for House Allocation with Existing Tenants," Cahiers de Recherches Economiques du Département d'économie 19.06, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:19.06
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    Cited by:

    1. Pycia, Marek & Ãœnver, M. Utku, 2020. "Arrovian Efficiency and Auditability in the Allocation of Discrete Resources," CEPR Discussion Papers 15377, C.E.P.R. Discussion Papers.
    2. Julien Combe, 2023. "Reallocation with priorities and minimal envy mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 551-584, August.
    3. Yao Cheng & Di Feng, 2025. "On fairness of multi-center allocation problems," Papers 2509.21812, arXiv.org, revised Oct 2025.
    4. Mandal, Pinaki & Roy, Souvik, 2021. "Strategy-proof Allocation of Indivisible Goods when Preferences are Single-peaked," MPRA Paper 105320, University Library of Munich, Germany.
    5. Ekici, Özgün & Sethuraman, Jay, 2024. "Characterizing the TTC rule via pair-efficiency: A short proof," Economics Letters, Elsevier, vol. 234(C).

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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
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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