We obtain a characterization of feasible, Bayesian, multi-item multi-bidder mechanisms with independent, additive bidders as distributions over hierarchical mechanisms. Combined with cyclic-monotonicity our results provide a complete characterization of feasible, Bayesian Incentive Compatible mechanisms for this setting.

Our characterization is enabled by a novel, constructive proof of Border's theorem [Border ... more >>>

We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first setting, we need that each bidder's values for the items are sampled from a ... more >>>