CORC Report TR-2006-01: Short Version Optimal Procurement Mechanisms for Divisible Goods with Capacitated Suppliers

The literature on procurement auctions typically assumes that the suppliers are uncapacitated (see, e.g. Dasgupta and Spulber, 1990; Che, 1993). Consequently, these auction mechanisms award the contract to a single supplier. We study mechanism design in a model where suppliers have limited production capacity, and both the marginal costs and the production capacities are private information. We provide a closed form solution for the revenue maximizing direct mechanism when the distribution of the cost and production capacities satisfies a modified regularity condition (Myerson, 1981). We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers, i.e. symmetric environment. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation. Examples of such problems include monopoly pricing with adverse selection and forward auctions.