Information Design of a Delegated Search

A principal delegates a sequential search with finite search opportunities to an agent, who bears the search cost and controls how far to search. The termination payoff is split between them according to a prespecified proportion. In our setting, only the principal can evaluate the search outcomes and design a policy to decide what information to provide to the agent after each search. Formulating the principal’s problem as a dynamic information design, we obtain a complete analytical characterization of the principal’s optimal information policy featuring a sequence of deterministic acceptance standards. The agent is simply recommended to and will voluntarily continue the search if and only if the current termination payoff falls below the corresponding standard prespecified at the beginning of the search. This policy offers an easy-to-implement prescriptive guideline for how information can be used as an incentive device in delegated search, especially absent pecuniary instruments. For nonrecallable search, the acceptance standards are informative, descending, and determined recursively as the optimal stopping thresholds that the principal would employ if the principal were to search directly at a shadow cost. In contrast, for recallable search, the optimal policy features a regime change: for the first cutoff number of search opportunities, the principal can set a constant, possibly uninformative acceptance standard that would be attainable in a costless search; after the cutoff opportunity, the principal sets a sequence of descending acceptance standards, each independently determined by equating the agent’s marginal perceived return from one additional search with the cost.

This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis.

Funding: This work was supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 [Grant MOE-2019-T3-1-010].

Supplemental Material: The online appendices are available at https://doi.org/10.1287/mnsc.2024.05925.