Combinatorial Auctions with Budgets

We consider budget constrained combinatorial auctions where bidder i has a private value vi for each of the items in some set Si, agent i also has a budget constraint bi. The value to agent i of a set of items R is |R ∩ Si| · vi. Such auctions capture adword auctions, where advertisers offer a bid for those adwords that (hopefully) reach their target audience, and advertisers also have budgets. It is known that even if all items are identical and all budgets are public it is not possible to be truthful and efficient. Our main result is a novel auction that runs in polynomial time, is incentive compatible, and ensures Pareto-optimality. The auction is incentive compatible with respect to the private valuations, vi, whereas the budgets, bi, and the sets of interest, Si, are assumed to be public knowledge. This extends the result of Dobzinski et al. [3, 4] for auctions of multiple identical items and public budgets to single-valued combinatorial auctions with public budgets. Tel Aviv University; Research partially supported by a grant from the Israel Academy of Sciences Sapienza University of Rome University of New Mexico; Research was partially supported by NSF CAREER Award 0644058 and NSF CCR-0313160 University of Warsaw