Optimal procurement mechanisms for divisible goods with capacitated suppliers

Procurement auction literature typically assumes that the suppliers are uncapacitated [see, e. g. Dasgupta and Spulber in Inf Econ Policy 4:5-29, 1990 and Che in Rand J Econ 24(4):668-680, 1993]. Consequently, the 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 in Math Oper Res 6(1):58-73, 1981]. We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation.