The Value of Information in Stopping Problems

Lehrer, Ehud; Wang, Tao

Abstract

We consider stopping problems in which a decision maker (DM) faces an unknown state of nature and decides sequentially whether to stop and take an irreversible action, or pay a fee and obtain additional information. We discuss the value and quality of information. The former is the maximal discounted expected total payment the DM can generate under a history-dependent fee scheme. We show that among all history-dependent fee schemes, the upfront fee scheme (as opposed, for instance, to pay-for-use) is optimal: it achieves the value of information. The effects on the optimal strategy of obtaining information from a more accurate source and of having a higher discount factor are distinct, as far as expected stopping time and its distribution are concerned. However, these factors have a similar effect in that they both enlarge the set of cases in which the optimal strategy prescribes waiting.

Citation

Lehrer, E., & Wang, T. (2023). The Value of Information in Stopping Problems. Economic Theory, 78, 619–648. https://doi.org/10.1007/s00199-023-01543-8

• Journal Article Type: Article
• Acceptance Date: Nov 15, 2023
• Online Publication Date: Dec 26, 2023
• Publication Date: Dec 26, 2023
• Deposit Date: Aug 16, 2023
• Publicly Available Date: Dec 27, 2024
• Journal: Economic Theory
• Print ISSN: 0938-2259
• Electronic ISSN: 1432-0479
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 78
• Pages: 619–648
• DOI: https://doi.org/10.1007/s00199-023-01543-8
• Public URL: https://durham-repository.worktribe.com/output/1719495