Information Design of a Delegated Search

48 Pages Posted: 20 Oct 2022 Last revised: 28 Nov 2022

See all articles by Yangge Xiao

Yangge Xiao

National University of Singapore, Institue of Operations Research and Analytics

Zhenyu Hu

National University of Singapore (NUS)

Shouqiang Wang

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: October 15, 2022

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.

Keywords: sequential decision making, dynamic Bayesian persuasion, principal-agent, threshold policy, recommendation

Suggested Citation

Xiao, Yangge and Hu, Zhenyu and Wang, Shouqiang, Information Design of a Delegated Search (October 15, 2022). Available at SSRN: https://ssrn.com/abstract=4249165 or http://dx.doi.org/10.2139/ssrn.4249165

Yangge Xiao

National University of Singapore, Institue of Operations Research and Analytics ( email )

Institute of Operations Research and Analytics
Innovation 4.0, #04-01, 3 Research Link
117602
Singapore

Zhenyu Hu

National University of Singapore (NUS) ( email )

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

Shouqiang Wang (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
377
Abstract Views
975
Rank
144,449
PlumX Metrics