A Simple Approach to Analyzing Asymmetric First Price Auctions

In this paper, we propose a new approach to analyzing asymmetric first price auctions. Specifically, we examine winning probabilities, exploiting the connection between winning probabilities and payoffs known from mechanism design. This circumvents the need to look directly at bidding strategies, which are generally complex. We derive new results, and more easily prove almost all existing results. The approach also sheds light on hitherto unexamined types of asymmetry. Moreover, the method also applies to asymmetric all-pay auctions, where all buyers pay their own bid, and about which little is currently known.