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)).
Case 3: |p1 −p2| ≤ ǫ2 Let us argue that almost no buyers are of type (1) or type (2)
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Multi-Unit Combinatorial Prophet Inequalities
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)).