The Value of Information in Some Variations of the Stopping Problem

In stopping problems, the decision maker receives a sequence of candidates and decides whether to select the current candidate and thereby stop the search or whether to continue surveying. Some examples include searching for an apartment, selecting an employee for a job, or choosing a new product or service from a sequence of vendors. Most of the literature on stopping problems assumes that the decision maker can perfectly evaluate the candidate when surveyed. We consider practical variations where surveying a candidate may provide no further information or imperfect information about its value. We show how the stopping problem can be considered an extension of the two-action (go/no-go) problem and present threshold optimal policies for the general problem. For the case where surveying candidates provides no further information and the uncertain values of candidates are normally distributed, we present analytical results that highlight how the value of information is affected by the parameters. With the help of an illustrative example, we demonstrate how a model that ignores sequential decisions could potentially severely underestimate the value of information. We also present a data-driven application of our results by studying the value of reports to a potential used car buyer.