DECISION-ANALYSIS WITH INCOMPLETE UTILITY AND PROBABILITY INFORMATION

An approach to the solution of decision analysis problems under uncert ainty with imprecise and incomplete information is presented. The meth odology is designed for cases in which payoffs (conditional on the sta te of nature) are known precisely, but only limited or imprecise proba bility 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 e quivalent for a simple lottery, any known relationships between probab ilities of states of nature, and a series of strict preferences betwee n pairs of vectors of conditional payoffs. We assume an exponential ut ility function with unknown parameter. The method proceeds by sequenti ally eliciting preferences, new bounds on probabilities and/or the cer tainty equivalent, and new relationships among probabilities until the problem is solved. The methodology is demonstrated through a two-stat e and a three-state example which illustrate the effects of the progre ssive elicitation of additional information.