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The core in the housing market model with fractional endowments

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  • Jingsheng Yu
  • Jun Zhang

Abstract

We explore the core concept in a generalization of the housing market model where agents own fractional endowments while maintaining ordinal preferences. Recognizing that individuals are easier than coalitions to block an allocation, we adopt a definition in which individuals block an allocation if their received assignments do not first-order stochastically dominate their endowment, while a non-singleton coalition blocks an allocation if they can reallocate their endowments to obtain new assignments that first-order stochastically dominate their original assignments. Our findings show that, unlike the original model, the strong core may be empty, while the weak core is nonempty. The weak core always contains elements that satisfy equal treatment of equals, but it may not contain elements satisfying equal-endowment no envy.

Suggested Citation

  • Jingsheng Yu & Jun Zhang, 2025. "The core in the housing market model with fractional endowments," Papers 2508.11151, arXiv.org.
    • Handle: RePEc:arx:papers:2508.11151
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    File URL: http://arxiv.org/pdf/2508.11151
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    References listed on IDEAS

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    1. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
    2. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading mechanisms for resource exchange in market design," Papers 2005.06878, arXiv.org, revised Aug 2025.
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