Informational Size and Efficient Auctions

Abstract

We develop an auction model for the case of interdependent values and multidimensional signals in which agents' signals are correlated. We provide conditions under which a modification of the Vickrey auction which includes payments to the bidders will result in an ex post efficient outcome. Furthermore, we provide a definition of informational size such that the necessary payments to bidders will be arbitrarily small if agents are sufficiently informationally small. The efficiency of market processes has been a central concern in economics since its inception. Auction mechanisms constitute a very important class of market processes, yet the analysis of auctions has typically focused on their revenue generating properties rather than their efficiency properties. This is partly due to the fact that, for many of the problems typically studied, efficiency is trivial. When bidders have private values, a standard Vickrey auction guarantees that the object will be sold to the buyer with the highest value for the object. In the case of pure common values-that is, when all buyers have the same value for the object-any outcome that with probability one assigns the object to some bidder will be efficient. The intermediate case in which bidders' values are not identical but may depend on other bidders' signals is more problematic. When bidders' values are interdependent in this way, any single bidder's value may depend on the information of other agents and, hence, he may not even know his own value. It is not clear what it would mean for an agent to bid his true value, even before we ask if it is optimal for him to do so. Several papers have studied efficient auctions with interdependent values and independent types.1 While this is a natural place to begin, the independence assumption is not compelling for many problems. A prototypical problem is one in which an object is to be sold, and individual bidders have private information about the object (say the quantity or quality of oil in a tract to be sold) that affects other agents' values for the object. When bidders' types include information about objective characteristics of the object being sold, their types will typically not be independent. When agents' types are statistically dependent, we show that there exist efficient auction mechanisms for interdependent value auction problems that are essentially Vickrey auctions augmented by payments to (not from) the agents. Most importantly, we link the