Bayesian combinatorial auctions

Abstract

Abstract. We study the following Bayesian setting: m items are sold to n sel¯sh bidders in m independent second-price auctions. Each bidder has a private valuation function that expresses complex preferences over all subsets of items. Bidders only have beliefs about the valuation func-tions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular valuation functions, then every Bayesian Nash equilibrium of the resulting game provides a 2-approximation to the op-timal social welfare. Moreover, we show that in the full-information game a pure Nash always exists and can be found in time that is polynomial in both m and n.