Another reason to choose the first-price auction
In this paper we derive equilibrium bidding functions for first-price and second-price auctions with private values when bidders have outside options. We then study bidding behaviour with the help of experiments. We find that bidders respond to outside options and to variations of common knowledge about competitors' outside options, though bidders in first-price auctions show more overbidding with outside options than without. In second-price auctions overbidding is not affected by outside options. As expected first-price auctions yield more revenue than second-price auctions. This revenue-premium is higher in the presence of outside options.