Abstract
We solve the optimal multi-dimensional mechanism design problem when either the number of bidders is a constant or the number of items is a constant. In the first setting, we need that the values of each bidder for the items are i.i.d., but allow different distributions for each bidder. In the second setting, we allow the values of each bidder for the items to be arbitrarily correlated, but assume that the bidders are i.i.d. For all ε textgreater 0, we obtain an efficient additive ε-approximation, when the value distributions are bounded, or a multiplicative (1–ε)-approximation when the value distributions are unbounded, but satisfy the Monotone Hazard Rate condition. When there is a single bidder, we generalize these results to independent but not necessarily identically distributed value distributions, and to independent regular distributions.
