Ascending Auctions with Multidimensional Signals

We study an ascending auction of an indivisible good in which agents observe multidimensional Gaussian signals about their valuation of the good. The equilibrium is solved using a two-step procedure. The first step is to project the signals into a one-dimensional equilibrium statistic. The second step is to solve for the equilibrium as if agents observed only the equilibrium statistic (and hence, as if agents observe one-dimensional signals). The solution method can also be applied to other trading mechanisms, including supply function competition. We provide predictions of ascending auctions that arise only when agents observe multidimensional signals. The first prediction is that an ascending auction may have multiple symmetric equilibria. Each equilibrium induces a different allocative efficiency and different profits for the seller. The second prediction is that, with multidimensional signals, public signals can be detrimental for profits (even in symmetric environments). In fact, a precise enough public signal can induce profits arbitrarily close to 0. The third prediction is that public signals increase the surplus generated by the auction. These predictions already arise in a model with two-dimensional signals that combines a classic model of private values and a classic model of common values. Hence, the only difference between the model we study and the classic models of ascending auctions is the multidimensionality of the information structure. JEL Classification: D40, D44, D47, D82, G14