Price Delegation with Learning Agents

Many firms delegate pricing decisions to sales agents that directly interact with customers. A premise behind this practice is that sales agents can gather informative signals about the customer's valuation for the good of interest. The information acquired through this interaction with the customer can then be used to make better pricing decisions. We study the underlying principal-agent problem that arises in such situations. In this setting, the agent can exert costly effort to learn a customer's valuation and then decide on the price to quote to the customer, whereas the firm needs to offer a contract to the agent to induce its desired joint learning and pricing behavior. We analyze two versions of this problem: a base model where there is a single customer and a single good, and a generalization where there are multiple customers and limited inventory of the good. For both problems, we find a family of contracts whose payoffs can approach first-best payoffs arbitrarily closely even if the agent has limited liability, that is, garners nonnegative payments in all states of the world, and shed light on the structure and implementation of such contracts. Under reasonable assumptions, these contracts can be implemented with commissions that are convex increasing in revenues up to some cap. These contracts continue to perform well under practical adjustments such as commissions with a revenue-sharing structure.