Optimal Agendas for Sequential Auctions for Common and Private Value Objects

Abstract

This paper analyzes sequential auctions for objects that have both common and private values. Existing work has studied sequential auctions for objects that are either exclusively common or private value. However, in many cases, an object has both features. Now, in such cases, the common value (which is the same for all bidders) depends on each bidder’s valuation of the object. But, generally speaking, a bidder cannot know the true common value, since it does not know how much the other bidders value it. On the other hand, a bidder’s private value is independent of the others’ private values. Given this, our objective is to study sequential auctions for heterogeneous objects that have both common and private values by treating each bidder’s information about the common value as uncertain. In so doing, we first determine equilibrium bidding strategies for each auction in a sequence. Then, since the total revenue from all the auctions in a sequence depends on the auction agenda (i.e., the order in which the objects are auctioned) we determine the optimal agenda (i.e., the one that maximizes total expected revenue across all the auctions in a sequence). Finally, we show that, for a given agenda, the total revenue is the same for first-price, second-price, and English auction rules.

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