Budget feasible mechanism design

Abstract

Budget feasible mechanism design studies procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most important questions in the field is "which valuation domains admit truthful budget feasible mechanisms with 'small' approximations (compared to the social optimum)?" Singer [35] showed that additive and submodular functions have a constant approximation mechanism. Recently, Dobzinski, Papadimitriou, and Singer [20] gave an O(log2n) approximation mechanism for subadditive functions; further, they remarked that: "A fundamental question is whether, regardless of computational constraints, a constant-factor budget feasible mechanism exists for subadditive functions."