Information Design of a Delegated Search

Département Information Systems et Operations Management

Intervenant: Shouqiang Wang (UT Dallas)

Salle Bernard Ramanantsoa

Abstract

A principal delegates a sequential search in finite horizon to an agent, who bears the search cost and controls when to terminate the search. Upon termination, the search payoff is split between the principal and agent. However, only the principal can evaluate each search outcome, whose value is thus unobservable to the agent. Leveraging this informational advantage, the principal designs an information policy to strategically provide the agent with some information about the search results over time. We obtain a complete analytical characterization of the principal’s optimal policy, which is fully prescribed by a sequence of deterministic acceptance standards, one for each period. The agent is recommended and voluntarily willing to continue the search if and only if the current termination payoff fails to meet that period’s standard. In particular, the principal gradually lowers the standard over time. When the search results are not recallable, the acceptance standards are informative and determined recursively across different periods as the optimal stopping thresholds that the principal would employ should she conduct each search by herself at a shadow cost. The shadow cost signifies how difficult it is for the principal to persuade the agent to conduct the search. When the search results are recallable, the optimal policy provides no information and the agent keeps searching up to a cutoff period, after which the acceptance standard in each subsequent period is determined independently of other periods by equating the agent’s search cost with his marginal return from an additional search in that period.