Revenue Submodularity

Shaddin Dughmi, Tim Roughgarden, Mukund Sundararajan

Abstract: We introduce revenue submodularity, the property that market expansion has diminishing returns on an auction’s expected revenue. We prove that revenue submodularity is generally possible only in matroid markets, that Bayesian-optimal auctions are always revenue-submodular in such markets, and that the VCG mechanism is revenue-submodular in matroid markets with IID bidders and “sufficient competition”. We also give two applications of revenue submodularity: good approximation algorithms for novel market expansion problems, and approximate revenue guarantees for the VCG mechanism with IID bidders.