Optimizing Offer Sets for Multi-Item Simultaneous Auctions: A Minimax Regret Approach

We examine the problem of identifying an optimal set of items to put up for sale (out of a larger set) in simultaneous sealed-bid auctions when pre-bidding item inspection or participation is costly, and the bidders' inspection budgets are limited. We first discuss how there can be uncertainty in the participation decisions of the bidders and how this uncertainty can impact the auctioneer's expected revenue. We then study the problem of identifying an optimal set of items. Here, we use a minimax regret criterion to deal with the uncertainty in bidder participation decisions. Our results show that it is possible to identify the optimal subset in polynomial time when each bidder's valuation for the items is additive and when the state space is polynomially bounded in size.