Decision Analysis with Incomplete Utility and Probability Information

An approach to the solution of decision analysis problems under uncertainty with imprecise and incomplete information is presented. The methodology is designed for cases in which payoffs (conditional on the state of nature) are known precisely, but only limited or imprecise probability and utility information is available regarding a decision maker's beliefs and tastes. A decision maker provides: conditional payoffs, (optionally) bounds on state probabilities, bounds on the certainty equivalent for a simple lottery, any known relationships between probabilities of states of nature, and a series of strict preferences between pairs of vectors of conditional payoffs. We assume an exponential utility function with unknown parameter. The method proceeds by sequentially eliciting preferences, new bounds on probabilities and/or the certainty equivalent, and new relationships among probabilities until the problem is solved. The methodology is demonstrated through a two-state and a three-state example which illustrate the effects of the progressive elicitation of additional information.