Еxperimental development of criteria for choice under uncertainty with estimates that, like Savage's rule, take into account the opportunity cost of action alternatives

Abstract

The article addresses the problem of improving decision-making rules under conditions of uncertainty within the framework of decision theory, with a particular focus on economic and managerial decision-making. The authors argue that the wide variety of classical decision rules—such as those proposed by Wald, Laplace, Hurwicz, Savage, and Bayes—demonstrates not only the absence of a universal decision-making model, but also the fundamental impossibility of applying a single rule to all types of decision problems. Each rule possesses specific advantages and limitations depending on the nature of available information, the type of uncertainty involved, and the characteristics of the decision-maker.

Special attention is paid to economic decisions, for which the concept of opportunity cost plays a crucial role. It is shown that the Savage decision rule uniquely incorporates opportunity losses by constructing and evaluating a regret matrix prior to aggregation. On this basis, the authors develop the idea of distinguishing a specific subclass of decision rules that compare alternatives before calculating an integral criterion. Such rules may be interpreted as measures of economic efficiency rather than mere effectiveness.

The theoretical foundation of the study is built upon an analogy with cooperative (non-strategic) game theory, where social welfare functions are divided into social utility functions and social choice functions. The authors propose transferring this classification logic to decision rules used in games against nature and strategic games. Accordingly, decision criteria are divided into those that aggregate outcomes based solely on the internal values of payoff vectors, and those that involve preliminary comparisons between alternatives. It is demonstrated that among classical decision rules, only the Savage rule clearly belongs to the latter category, which highlights the need to expand this subclass.

The article examines the Zubkova decision rule as an example of combining the procedures of the Savage and Laplace rules and illustrates its distinctive features using numerical payoff matrices. The analysis shows that although several rules may lead to identical recommendations regarding the best and worst alternatives, they often differ in ranking intermediate options, which becomes increasingly significant as the dimensionality of payoff matrices grows.

Furthermore, the authors propose a series of experimental decision rules based on transforming standard payoff matrices into binary matrices of effects. This transformation relies on a threshold coefficient calculated as the average value of all payoffs in the matrix. Based on this approach, rules involving binary evaluation, as well as reinforcement and weakening of payoff vectors with respect to the opponent’s interests, are introduced and tested. The results indicate that while such rules may reduce uncertainty in certain cases, they often lead to insufficient differentiation of alternatives and may even distort the decision-maker’s preferences in specific configurations.

The study concludes that the proposed experimental rules should not be considered final decision-making instruments. However, they represent an important exploratory step toward the development of a broader class of decision rules that explicitly account for opportunity costs. Future research should focus on simulation modeling, systematic comparison of decision outcomes across different rules, and the identification of conditions under which particular rules provide the most reliable and economically meaningful recommendations.