Multi-Dimensional Bid Improvement Algorithm for Simultaneous Auctions

Abstract

Bidding for multi-items in simultaneous auctions raises challenging problems. In multi-auction settings, the determination of optimal bids by potential buyers requires combinatorial calculations. While an optimal bidding strategy is known when bidding in sequential auctions, only suboptimal strategies are available when bidding for items being sold in simultaneous auctions. We investigate a multi-dimensional bid improvement scheme, motivated by optimization techniques, to derive optimal bids for item bundles in simultaneous auctions. Given a vector of initial bids, the proposed scheme systematically improves bids for each item. Such multi-dimensional improvements result in locally optimal bid vectors. Globally optimal bid vectors are guaranteed in the limit for infinite restarts. For ease of presentation we use two-item scenarios to explain the working of the algorithm. Experimental results show polynomial complexity of variants of this algorithm under different types of bidder valuations for item bundles.