An Analysis of Sequential Auctions for Common and Private Value Objects

Abstract

Sequential auctions are an important mechanism for buying/selling multiple objects. Now existing work in the area has studied sequential auctions for objects that are exclusively either common value or private value. However, in many real-world cases an object has both features. Also, in such cases, the common value depends on how much each bidder values the object. Moreover, a bidder generally does not know the true common value (since it may not know how much the other bidders value it). Given this, our objective is to study settings that have both common and private value elements by treating each bidder’s information about the common value as uncertain. Each object is modelled with two signals: one for its common value and the other for its private value. The auctions are conducted using English auction rules. For this model, we first determine equilibrium bidding strategies for each auction in a sequence. On the basis of this equilibrium, we find the expected revenue and the winner’s expected profit for each auction. We then show that even if the common and private values of objects are distributed identically across all objects, the revenue and the winner’s profit are not the same for all of them. We show that, in accordance with Ashenfelter’s experimental results [1], the revenue for our model can decline in later auctions.