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The core of Shapley-Scarf markets with full preferences

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  • Jun Zhang

Abstract

We examine core concepts in the classical model of Shapley and Scarf (1974) under full preferences. Among the standard concepts, the strong core may be empty, whereas the nonempty weak core may be overly large and contain inefficient elements. Our main findings are: (1) The exclusion core of Balbuzanov and Kotowski (2019) -- a recent concept outperforming standard concepts in complex environments under strict preferences -- can also be empty, yet it is more often nonempty than the strong core. (2) We introduce two new core concepts, respectively built on the exclusion core and the strong core. Both are nonempty and Pareto efficient, and coincide with the strong core whenever it is nonempty. (3) These core concepts are ordered by set inclusion, with the strong core as the smallest and the weak core as the largest.

Suggested Citation

  • Jun Zhang, 2025. "The core of Shapley-Scarf markets with full preferences," Papers 2511.21158, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2511.21158
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    References listed on IDEAS

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    1. Wako, Jun, 1984. "A note on the strong core of a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 189-194, October.
    2. Jun Zhang, 2025. "Consistent solutions to the allocation of indivisible objects with general endowments," Papers 2511.21155, arXiv.org, revised Dec 2025.
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