The Impact of the Structure of the Payoff Matrix on the Final Decision made Under Uncertainty

Abstract

When decisions are made under uncertainty (DMUU), the decision maker either disposes of an interval of possible profits for each alternative (the interval DMUU) or disposes of a discrete set of payoffs for each decision and then the amount of the profit related to a given alternative depends on the state of nature (the scenario DMUU). Existing methods, used to generate the ranking of decisions and applied to the second problem mentioned, take, to a different extent, into consideration how particular profits assigned to alternatives are ordered in the payoff matrix and what the position of a given outcome is in comparison with other outcomes for the same state of nature. The author proposes and describes several alternative procedures that enable connecting the structure of the payoff matrix with the selected decision. These methods are adjusted to the purpose and the nature of the decision maker. They refer to the Savage’s approach, to the maximin joy criterion, to the normalization technique and to some elements used in expected utility maximization and prospect theory.