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The value of information in stopping problems

Author

Listed:
  • Ehud Lehrer

    (Durham University)

  • Tao Wang

    (Capital University of Economics and Business)

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.

Suggested Citation

  • Ehud Lehrer & Tao Wang, 2024. "The value of information in stopping problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 619-648, September.
    • Handle: RePEc:spr:joecth:v:78:y:2024:i:2:d:10.1007_s00199-023-01543-8
    DOI: 10.1007/s00199-023-01543-8
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    References listed on IDEAS

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    More about this item

    Keywords

    Stopping problem; Value of information; Optimal fee scheme; Information quality; Patience;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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