The value of perfect information for the problem: a sensitivity analysis

Abstract This paper examines problems in decision theory where the number of alternatives and states of nature are finite. Previous studies have defined the concept of “the value of perfect information for the problem” ( VPIP ). This metric allows us to obtain an upper bound on the amount a decision-maker would be willing to pay for perfect information under the specific conditions of a problem. This bound is particularly important when the decision is unrepeatable, providing a more accurately adjusted measure than the one traditionally obtained with “the expected value of perfect information” ( EVPI ). Supported by linear programming, this work proposes a sensitivity analysis of these bounds by seeking to identify the intervals in which the problem values can vary without essentially modifying the structure of the problem. Specifically, the study aims to determine how this variation might affect the EVPI and VPIP bounds, as well as the difference in the price a decision-maker would be willing to pay for perfect information if any of the problem values were altered. By identifying alternatives and scenarios taking into account the role they play in the problem, this research classifies the data involved in a finite decision problem to ensure the conclusions can be understood as generally as possible. Although the proposed sensitivity analysis is applied to the oil-drilling problem, a classic in decision theory, the conclusions of this work have potential applications in improving environmental decision-making processes.