The simple economics of approximately optimal auctions

Saeed Alaei, Hu Fu, Nima Haghpanah, Jason Hartline

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Scopus citations

Abstract

The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasi-linear utility and single-dimensional preferences, Bulow and Roberts [1] show that the optimal auction of Myerson [2] is in fact optimizing marginal revenue. In particular Myerson's virtual values are exactly the derivative of an appropriate revenue curve. This paper considers mechanism design in environments where the agents have multi-dimensional and non-linear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal, and furthermore, there is sometimes no direct way to implement the marginal revenue maximization mechanism. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal (by identifying an important condition that we call revenue linearity), we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from an ideal one (i.e., where marginal revenue maximization is optimal). Because the marginal revenue mechanism is optimal for well-studied single-dimensional agents, our generalization immediately extends many approximation results for singledimensional agents to more general preferences. Finally, one of the biggest open questions in Bayesian algorithmic mechanism design is in developing methodologies that are not brute-force in size of the agent type space (usually exponential in the dimension for multi-dimensional agents). Our methods identify a subproblem that, e.g., for unitdemand agents with values drawn from product distributions, enables approximation mechanisms that are polynomial in the dimension.

Original languageEnglish (US)
Title of host publicationProceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
Pages628-637
Number of pages10
DOIs
StatePublished - 2013
Event2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States
Duration: Oct 27 2013Oct 29 2013

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Other

Other2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013
CountryUnited States
CityBerkeley, CA
Period10/27/1310/29/13

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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