Dominant-strategy and Bayesian incentive compatibility in multi-object trading environments

When a single-object is to be traded, Bayesian and dominant-strategy incentive compatible mechanisms are interim-utility equivalent in independent, private-values environments; in the same environments, the equivalence breaks down when there are many distinct, indivisible objects to trade. We show that the fixed supply of each type of good imposes strong restrictions on the mechanisms that can be implemented. These restrictions can then be used to determine whether a given Bayesian mechanism has an equivalent dominant-strategy mechanism in a multi-unit model.