Understanding multi-dimensional mechanism design. 1 The Model Let M = {1, . . . , m} be a finite set of agents. Every agent has private information, which can be multi-dimensional. This is called his type. The space from which an agent draws his type is called his type space. Let Ti denote the type space of agent i ∈ M . We assume Ti ⊆ R n for some integer n ≥ 1. Let T m = ×mi=1Ti. Also, denote...

We characterize incentive compatibility in multi-unit auctions with multi-dimensional types. An allocation mechanism is incentive compatible if and only if it is nondecreasing in marginal utilities (NDMU). The notion of incentive compatibility we adopt is dominant strategy in private value models and ex post incentive compatibility in models with interdependent values. NDMU is the following req...

We consider locally incentive compatible mechanisms with deterministic allocation rules and transfers with quasilinear utility. We identify a rich class of type spaces, which includes the single peaked type space, where local incentive compatibility does not imply incentive compatibility. Our main result shows that in such type spaces, a mechanism is locally incentive compatible and payment-onl...