Search Results (6)

Decision-making theory has developed over many decades at the intersection of economics, mathematics, psychology, and engineering. Its classical foundations include Bernoulli’s expected utility theory, von Neumann and Morgenstern’s rational choice theory, and the criteria proposed by Savage, Wald, Hurwicz, and others. However, in real-world contexts, decisions are made under uncertainty, incompleteness, and unreliability of information, which classical approaches do not adequately address. To overcome these limitations, modern multi-criteria decision-making methods such as Analytic Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VlseKriterijumska Optimizacija I Kompromisno Resenje (Compromise solution approach) (VIKOR), and ELimination Et Choix Traduisant la REalité (Elimination and Choice Expressing Reality) (ELECTRE), as well as their fuzzy and Z-number extensions, are widely applied to the modeling and evaluation of complex systems. These Z-number extensions are based on the concept of Z-numbers introduced by Lotfi Zadeh in 2011 to formalize higher-order uncertainty. This study introduces the Z-Regret principle, which extends Savage’s regret criterion through the use of Z-numbers. Supported by Rafik Aliev’s mathematical justifications concerning arithmetic operations on Z-numbers, the model evaluates regret not only as a loss relative to the best alternative but also by incorporating the degree of confidence and reliability of this evaluation. Calculations for the selection of digital advertising platforms in terms of performance assessment under various scenarios demonstrate that the Z-Regret principle enables more stable and well-founded decision-making under uncertainty. Full article

The risk of lending money collected from savers is that it leaves banks liable to default with depositors if events (and hence repayment demands) become ‘abnormal’. Even though international and national regulation has been introduced to ensure that a certain level of capital is retained by banks, such regulation can be subverted. The current system of international regulation based on the Basel III agreements does not stipulate a standardised approach for inspection frequency or penalty magnitude. This leaves the potential for regulatory arbitrage. The scientific value of an analysis to optimise regulatory efficiency and reduce such arbitrage is therefore considerable. This work therefore assesses the results of the empirical testing of a model based on the Von Neumann–Morgenstern utility function and consequently proposes that this model be used as a basis for standardising capital adequacy limit infraction penalties on an international level to prevent regulatory arbitrage. A survey is undertaken in order to test the responses of participants on the level of penalty which would deter them from regulatory transgression under different theorised levels of profit and probability of discovery. Based on the responses of two distinct subject groups (‘bankers’ and ‘non-bankers’) in different scenarios of hypothetical capital adequacy violation, the Von Neumann–Morgenstern utility function is reviewed against empirical results and revealed to show a semi-strong correlation. Lastly, the analysis reveals the striking similarities of the two groups’ responses, posing regulatory implications for the industry. Full article

Expected utility theory (EUT) is currently the standard framework which formally defines rational decision-making under risky conditions. EUT uses a theoretical device called von Neumann–Morgenstern utility function, where concepts of function and random variable are employed in their pre-set-theoretic senses. Any von Neumann–Morgenstern utility function thus derived is claimed to transform a non-degenerate random variable into its certainty equivalent. However, there can be no certainty equivalent for a non-degenerate random variable by the set-theoretic definition of a random variable, whilst the continuity axiom of EUT implies the existence of such a certainty equivalent. This paper also demonstrates that rational behaviour under utility theory is incompatible with scarcity of resources, making behaviour consistent with EUT irrational and justifying persistent external inconsistencies of EUT. A brief description of a new paradigm which can resolve the problems of the standard paradigm is presented. These include resolutions of such anomalies as instant endowment effect, asymmetric valuation of gains and losses, intransitivity of preferences, profit puzzle as well as the St. Petersburg paradox. Full article

The development of small-scale hydroelectric power plants in Norway is determined by natural conditions, policies, attitudes and property rights. The owner of the river is the central decision maker. It is he/she who decides whether he/she will develop the power plant himself/herself, whether he/he wants to enter into a contract with an external investor and let him/her develop the power plant, whether he/she will sell his/her property rights or postpone the decisions. All available choices will involve risk. In order for him/her to make the best choice, he/she must find the certainty equivalent to each of the choices and choose the one with the highest certainty equivalent. To find the certainty equivalent, we use the utility theory of John von Neumann and Oskar Morgenstern. The owner of the river makes the decision that gives him/her the greatest utility when both economic and non-economic effects are assessed within the opportunity set made by the local and the central authorities. Full article

This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Full article

A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed. Full article