Chapter

Auctions, Market Mechanisms and Their Applications

Volume 14 of the series Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering pp 89-91

Revenue Submodularity

  • Shaddin DughmiAffiliated withDepartment of Computer Science, Stanford University
  • , Tim RoughgardenAffiliated withDepartment of Computer Science, Stanford University
  • , Mukund SundararajanAffiliated withDepartment of Computer Science, Stanford University

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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.