Optimal Agendas for Sequential English Auctions with Private and Common Values

Abstract

This paper studies how to relax the restrictions on bidders in two sequential English auctions. Existing work has showed that it is optimal for the auctioneer to auction objects in the decreasing order of the dispersion of the order statistics of the surpluses. But they assume each bidder can win at most one object. However, in many cases, each bidder needs more than one object and the objects almost affect each other. Given this, the settings that have both common and private value elements by allowing each bidder winning more than one object are studied here. Firstly, the single object model is extended to two objects without the limitation that a bidder can win at most one object. Secondly, the equilibrium bidding strategies for each auction in a sequence are described, the selling prices and winner’s total expected profits of different agendas are analyzed. Thirdly, the optimal agendas are determined. Finally, we make two experiments, one validates that it may be the optimal agenda either by increasing order or decreasing order of the dispersion of the order statistics of the surpluses, the other display the changing trend of the optimal agenda.