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<p>We study allocation problems in non-convex domains where the valuation of a bundle of objects is determined by the maximum valuation among the objects in the bundle. We establish that an allocation rule is implementable if and only if it satisfies a well-known and intuitive condition known as weak monotonicity, also referred to as 2-cycle monotonicity.</p>

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Characterizing implementability via weak monotonicity on unit demand valuation domains

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Satish Agarwal,
  • Souvik Roy

摘要

We study allocation problems in non-convex domains where the valuation of a bundle of objects is determined by the maximum valuation among the objects in the bundle. We establish that an allocation rule is implementable if and only if it satisfies a well-known and intuitive condition known as weak monotonicity, also referred to as 2-cycle monotonicity.