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<p>We consider the problem of stochastically allocating <i>n</i> indivisible objects to <i>n</i> agents when each agent assigns cardinal utility values to the objects. In this context, Zhou (<CitationRef CitationID="CR15">1990</CitationRef>) 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.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年5月13日

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  • Hidekazu Anno

摘要

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.