Event Title

Smoothness As A Characterization of Price Of Anarchy in Auctions

Location

Virtual presentation

Document Type

Presentation

Start Date

4-27-2020 8:00 AM

End Date

5-2-2020 5:00 PM

Abstract

Auctions are often designed with the goal of maximizing social welfare, which is a combination of the auctioneer’s revenue with the utility of bidders. The notion of Price of Anarchy captures the worst-case loss in social welfare caused by the selfish behavior of bidders, making it useful to consider before deploying a given mechanism. Determining the Price of Anarchy for arbitrary auctions is difficult, making it helpful to analyze auction performance with alternative tools such as Smoothness, the main subject of our research. We prove that in certain settings, Smoothness fully characterizes Price of Anarchy. Additionally, we prove that computing Smoothness and Price of Anarchy are NP-hard.

Keywords:

Computer science, Computational economics, Auction, Game theory, Price of anarchy, Bidders, Smoothness, Revenue covering, Linear programming, Hypergraph, Set system, Threshold, Highest-bids-win, Single-minded combinatorial auction, Computational complexity, Worst-case analysis

Notes

Click here to view this presentation at the Office of Undergraduate Research website from April 27-May 2, 2020.

Major

Computer Science; Mathematics

Project Mentor(s)

Cindy Frantz, Psychology
Catherine Robinson-Hall, The Williams-Mystic Maritime Studies Program

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Apr 27th, 8:00 AM May 2nd, 5:00 PM

Smoothness As A Characterization of Price Of Anarchy in Auctions

Virtual presentation

Auctions are often designed with the goal of maximizing social welfare, which is a combination of the auctioneer’s revenue with the utility of bidders. The notion of Price of Anarchy captures the worst-case loss in social welfare caused by the selfish behavior of bidders, making it useful to consider before deploying a given mechanism. Determining the Price of Anarchy for arbitrary auctions is difficult, making it helpful to analyze auction performance with alternative tools such as Smoothness, the main subject of our research. We prove that in certain settings, Smoothness fully characterizes Price of Anarchy. Additionally, we prove that computing Smoothness and Price of Anarchy are NP-hard.