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As X(1) < k, we in fact sell X copies here and run out of copies for the first item

When X ∈ [k, 2k), X(1,2) ≥ k, we send buyers of type (1) first, then of type (1 , 2)

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Multi-Unit Combinatorial Prophet Inequalities

cs.GT · 2025-05-21 · conditional · novelty 8.0

For XOS buyers with k copies per item, supply-based posted pricing obtains a 1-(k/(k+1))^k competitive ratio, and dynamic pricing obtains 1-O(sqrt(log k/k)).

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  • Multi-Unit Combinatorial Prophet Inequalities cs.GT · 2025-05-21 · conditional · none · ref 3

    For XOS buyers with k copies per item, supply-based posted pricing obtains a 1-(k/(k+1))^k competitive ratio, and dynamic pricing obtains 1-O(sqrt(log k/k)).