We consider budget constrained combinatorial auctions where bidder i has a private value v_i, a budget b_i, and is interested in all the items in S_i. The value to agent i of a set of items R is v_i times  the size of the intersection between R and S_i. Such auctions capture adword auctions, where advertisers offer a bid for ads in response to an advertiser-dependent set of adwords, and advertisers have budgets. It is known that even of 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 for such auctions when the valuations are private and the budgets are public knowledge. This extends the result of Dobzinski et al. (FOCS 2008) for auctions of multiple identical items and public budgets to single-valued combinatorial auctions with public budgets.

Joint work with Amos Fiat, Jared Saia, Piotr Sankowski