The value of information in stopping problems

Ehud Lehrer () and Tao Wang ()
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Ehud Lehrer: Durham University
Tao Wang: Capital University of Economics and Business

Economic Theory, 2024, vol. 78, issue 2, No 9, 619-648

Abstract: 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.

Keywords: Stopping problem; Value of information; Optimal fee scheme; Information quality; Patience (search for similar items in EconPapers)
JEL-codes: D81 D83 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00199-023-01543-8

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