The Value of Information in Stopping Problems

TL;DR

This paper analyzes the value of information in sequential stopping problems, showing that upfront fee schemes maximize information value and exploring how source accuracy and discount factors influence optimal strategies.

Contribution

It demonstrates that upfront fee schemes are optimal for maximizing information value and distinguishes effects of source accuracy and discounting on stopping strategies.

Findings

Upfront fee schemes yield the highest value of information.

Higher source accuracy and discount factors increase the likelihood of waiting.

Optimal strategies are affected differently by source accuracy and discounting.

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; pay a fee and obtain additional information; or wait without acquiring information. We discuss the value and quality of information. The former is the maximal discounted expected revenue the DM can generate. We show that among all history-dependent fee schemes, the upfront scheme (as opposed, for instance, to pay-for-use) is optimal: it generates the highest possible 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.