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Note on Gale’s conjecture in one-sided matching problems

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  • Hidekazu Anno

    (University of Tsukuba)

Abstract

We consider the problem of stochastically allocating n indivisible objects to n agents when each agent assigns cardinal utility values to the objects. In this context, Zhou (1990) demonstrates Gale’s conjecture in a stronger form: No rule is strategy-proof, ex ante efficient, and symmetric. We further strengthen this impossibility theorem by relaxing the requirement of symmetry. Consequently, we indicate that every strategy-proof and ex ante efficient rule satisfies neither symmetry nor the equal division lower bound.

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  • Hidekazu Anno, 2025. "Note on Gale’s conjecture in one-sided matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-12, June.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00937-3
    DOI: 10.1007/s00182-025-00937-3
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    References listed on IDEAS

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    1. Alva, Samson & Manjunath, Vikram, 2020. "The impossibility of strategy-proof, Pareto efficient, and individually rational rules for fractional matching," Games and Economic Behavior, Elsevier, vol. 119(C), pages 15-29.
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