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Linear Programming for Mechanism Design: An Application to Bidder Collusion at First-Price Auctions

Giuseppe Lopomo (glopomo***at***duke.edu)
Leslie Marx (marx***at***duke.edu)
Peng Sun (psun***at***duke.edu)

Abstract: We demonstrate the use of linear programming techniques in the analysis of mechanism design problems. We use these techniques to analyze the extent to which a first-price auction is robust to collusion when, contrary to some prior literature on collusion at first-price auctions, the cartel cannot prevent its members from bidding at the auction. In this case, cartels have been shown to be less profitable facing a first-price auction than facing other common auction formats, but we show the stronger result that in certain environments collusion at a first-price auction is not profitable at all. Our results suggest that first-price auctions are more robust to collusion than previously believed.

Keywords: mechanism design, auctions, collusion, linear program

Category 1: Other Topics (Game Theory )

Category 2: Applications -- OR and Management Sciences

Category 3: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Duke University working paper, March 2008

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Entry Submitted: 03/28/2008
Entry Accepted: 03/28/2008
Entry Last Modified: 04/28/2008

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