Improved Prophet Inequalities for Combinatorial Welfare Maximization with (Approximately) Subadditive Agents

Hanrui Zhang, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
We give a framework for designing prophet inequalities for combinatorial welfare maximization. Instantiated with different parameters, our framework implies (1) an O(log m / log log m)-competitive prophet inequality for subadditive agents, improving over the O(log m) upper bound via item pricing, (2) an O(D log m / log log m)-competitive prophet inequality for D-approximately subadditive agents, where D ∈ {1, ... , m-1} measures the maximum number of items that complement each other, and (3) as
more » ... a byproduct, an O(1)-competitive prophet inequality for submodular or fractionally subadditive (a.k.a. XOS) agents, matching the optimal ratio asymptotically. Our framework is computationally efficient given sample access to the prior and demand queries.
doi:10.4230/lipics.esa.2020.82 dblp:conf/esa/Zhang20 fatcat:4urerxq725d2voqx2a22f6gd6e