  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 complete characterization of dominant-strategy
incentive-compatible direct mechanisms where over-reporting the budget is not
possible. In several settings, reporting larger budgets can be made suboptimal
with a small randomized modification to the payments. We then derive a closely
related partial characterization for the general case where players can
arbitrarily misreport their private budgets. Immediate applications of these
results include simple characterizations for mechanisms with publicly-known
budgets and for mechanisms 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 bidders.
