Equilibrium strategies for multi-unit sealed-bid auctions with multi-unit demand bidders

Abstract

In most of the existing literature on multi-unit auctions, i.e. auctions selling several identical goods together, it is assumed that bidders demand a single item. Yet this assumption is not valid in most practical auction settings, as often bidders wish to purchase multiple goods. Computing equilibrium strategies in multi-unit uniform-price auctions for bidders with multi-unit demand is an open problem for almost two decades. It is known that they exist in pure strategies, but not how to compute them. Our work addresses this key open problem, when there are no complementarities. More specifically, we examine a model where each bidder's value for the units beyond the first are computed by multiplying the value for the first unit of the good (the most desired one) by preset weights, and then generalize this model by allowing these weights to be different for each participating bidder. We characterize the equilibria and compute equilibrium strategies for both mth and (m+1)th price sealed-bid auctions; then we give some examples examining the properties of these strategies in the process. We conduct experiments that show up to 25% improvement in the performance of trading agents using these strategies as opposed to some heuristic strategies previously used.