Optimal procurement mechanisms for divisible goods with capacitated suppliers

Abstract

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.

Procurement auctions with capacity constrained suppliers

“…This is because under a direct mechanism the buyer does not have to give any rents to the supplier for them to truthfully bid their capacity. We complement the work of Iyengar and Kumar (2008) by showing that an open descending price clock auction would make a similar allocation and payment as an optimal mechanism and hence is also optimal.…”

“…However, our work differs from Cantillon's work in the sense that asymmetry is not induced by buyer/supplier investments in cost improvements, rather asymmetry in our model is exogenous and arises due to suppliers having different capacities. Close to our model's setting, Iyengar and Kumar (2008) investigate an auction in which suppliers have limited and heterogeneous capacities. Their model assumes that both cost and capacity of suppliers is their private information.…”

Implementation in multidimensional dichotomous domains

“…This literature usually considers Bayes-Nash randomized implementation. The usual approach in this literature is to consider specific multidimensional domains (sometimes with relaxed incentive constraints) and then extend Myerson's methodology to such settings; see Armstrong (1996), Blackorby and Szalay (2007), Iyengar and Kumar (2008), Pai and Vohra (2010), and Manelli and Vincent (2007). Our optimal mechanism design looks at a different multidimensional domain with deterministic dominant strategy implementation.…”

“…Unlike Myerson (1981), who searched for an optimal mechanism in the single object auction case over all Bayesian incentive compatible and randomized mechanisms, we are searching over all DSIC and deterministic mechanisms. Most of the literature on optimal mechanism design in multidimensional type spaces also considers Bayes-Nash randomized implementation (for example, Iyengar andKumar 2008, andPai andVohra 2010). For single object auctions, this restriction is without loss of generality since the optimal mechanism is a DSIC and deterministic mechanism; see a more general result for the single object auction case in Manelli and Vincent (2010).…”

Revenue maximization in the dynamic knapsack problem

“…This feature allows a less cumbersome characterization of implementable policies that can be embedded in the dynamic analysis under certain conditions on the joint distribution of values and weights of the arriving agents. Other multidimensional mechanism design problems with restricted deviations in one or more dimensions have been studied by Blackorby and Szalay (2007), Che and Gale (2000), Iyengar and Kumar (2008), Kittsteiner and Moldovanu (2005), and Pai and Vohra (2009).…”