Sequential Procurement with Contractual and Experimental Learning

We study the design of sequential procurement strategies that integrate stochastic and strategic information. We consider a buyer who repeatedly demands a certain good and is unable to commit to long-term contracts. In each time period, the buyer makes a price offer to a seller who has private, persistent information regarding his cost and quality of provision. If the offer is accepted, the seller provides the good with a stochastic quality that is not contractible; otherwise, the buyer sources the good from a known outside option. The buyer can therefore learn from the (strategic) acceptance decisions taken by the seller, and from evaluations of the (stochastic) quality delivered whenever a purchase occurs. Hence, the buyer not only faces a tradeoff between exploration and exploitation, but also needs to decide how to explore: by facilitating quality observations, or by strategically separating seller types. We characterize the Perfect Bayesian Equilibria of this sequential interaction and show that the buyer’s equilibrium strategy consists of a dynamic sequence of thresholds on her belief on the seller’s type. In equilibrium, the buyer offers high prices that incentivize trade and quality experimentation at early stages of the interaction and, after gathering enough information (and if her belief is sufficiently low), she advances to offering low prices that may partially separate seller types. Contrasting the buyer’s strategy with two benchmark strategies designed to learn from each form of information in isolation, we identify the effect that strategic sellers may have on the buyer’s optimal strategy relative to more traditional learning dynamics, and establish that, paradoxically, when sellers are strategic, the ability to observe delivered quality is not always beneficial for the buyer.