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.
Duke University working paper, March 2008