Title: Large asymmetric first-price auctions – a boundary-layer approach
Most of auction theory concerns the case where all bidders are symmetric (identical). This is not because bidders are believed to be symmetric, but rather because the analysis of asymmetric auctions is considerably harder. For example, in the case of the first-price auction, the symmetric case is governed by a single ODE which is easy to solve explicitly. In contrast, the model for asymmetric first-price auction consists of n first-order nonlinearly coupled ODES with 2n boundary conditions and an unknown location of the right boundary, where n is the number of bidders. This nonstandard boundary value problem (BVP) is hard to analyze. Therefore, very little is known about its solutions.
In this talk we analyze this BVP when the number of bidders is large (n>>1). We show that the solutions develop a nonstandard boundary layer structure, and obtain explicit O(1/n^3) approximations. These approximations lead to a surprising asymptotic revenue equivalence result between asymmetric first-price and second-price auctions.
This is a joint work with Gadi Fibich and Arieh Gavious.