Monotonicity, Revenue Equivalence and Budgets.

Budget constraints are central to big business auctions. In Google's GSP keyword auction and other search engine advertising platforms, the bidders are required to specify their bids as well as their budget limits. We study multidimensional mechanism design in a common scenario where players have private information about their willingness to pay and their ability to pay. We provide a necessary and sufficient conditions for the dominant-strategy incentive-compatible implementability of direct mechanisms. Immediate applications of these results include simple characterizations for auctions with publicly-known budgets and for auctions without monetary transfers. The celebrated revenue equivalence theorem states that the seller's revenue for a broad class of standard auction formats and settings will be the same in equilibrium. Our main application is a revenue equivalence theorem for financially constrained multidimensional bidders.