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A new allocation rule for the housing market problem with ties

Author

Listed:
  • Xinsheng Xiong

    (Wuhan University
    Huaihua College)

  • Xianjia Wang

    (Wuhan University)

  • Kun He

    (Huazhong University of Science and Technology)

Abstract

We address a general housing market problem with a set of agents and a set of houses. Each agent has a weak ordinal preference list that allows ties on houses as well as an initial endowment; moreover, each agent wishes to reallocate to a better house on the housing market. In this work, we reduces the complexity of the family of top trading cycles algorithms by selecting a specific house from the preferred set during the trading phase. The rule of construction digraphs is used to select an appropriate house. Based on these digraphs, we propose an extended top trading cycles algorithm with complexity $$O(n^{2} r)$$ O ( n 2 r ) , where $$n$$ n is the number of agents and $$r$$ r is the maximum length of ties in the preference lists. The algorithm complexity is lower than that of the state-of-the-art algorithms. We show that the proposed algorithm is individually rational, Pareto efficient, and strategy-proof. It thus overcomes the limitations of a classic top trading cycles algorithm, and features Pareto efficiency and strategy-proofness on the weak preference domain.

Suggested Citation

  • Xinsheng Xiong & Xianjia Wang & Kun He, 2022. "A new allocation rule for the housing market problem with ties," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 98-115, January.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00727-z
    DOI: 10.1007/s10878-021-00727-z
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    References listed on IDEAS

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    Cited by:

    1. Emilio Guaman & Juan Pablo Torres-Martinez, 2023. "Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences," Working Papers wp547, University of Chile, Department of Economics.

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