Expected utility in decision-making situations with random in a broad sense consequences

Authors

  • V. I. Ivanenko Кафедра математичного моделювання економічних систем Національного технічного університету України "КПІ", Київ, Ukraine

Abstract

An extension of the expected utility theorem for decision-making situations with random in a broad sense consequences is proposed. The statistical regularity of a corresponding random phenomenon is a family of finitely additive probability measures. This family has an objective origin and taken as a whole describes the regularity of a random phenomenon. Statistical regularities on the set of consequences correspond to decisions. Natural conditions on a preference relation on the set of all statistical regularities are proposed. It is shown, that they are necessary and sufficient for the existence and uniqueness of the utility functional that is a minimum of the expected utility of the elements of a statistical regularity. The result is applied to solving decision-making problems, measuring the information content of an xperiment and the uncertainty of a decision-making situation.

Author Biography

V. I. Ivanenko, Кафедра математичного моделювання економічних систем Національного технічного університету України "КПІ", Київ

Іваненко Віктор Іванович,

професор, доктор технічних наук, професор кафедри математичного моделювання економічних систем Національного технічного університету України "КПІ", Київ

References

Neyman Dzh., Morgenshtern O. Teoriya igr i ekonomicheskoye povedeniye: Per. s angl. — M.: Nauka, 1970. — 707 s.

Bouyssou D., Dubois D., Prade H., Pirlot M. Decision-Making Process: Concepts and methods. — NY: John Wiley & Sons, 2010. — 928 p.

Quiggin J. A theory of anticipated utility // Journal of Economic Behavior and Organization. — 1982. — 3. — P. 323–343.

Jaffray J.-Y. Linear utility theory for belief functions // Operation Research Letters. — 1989. — 8, № 2. — P. 107–112.

Savage L.J. The foundations of statistics. — NY: Wiley & Sons, 1954. — 294 p.

Ivanenko V.I., Labkovskiy V.А. Ob odnom klasse pravil vybora kriteriya // DАN SSSR. — 1986. — 287, № 3. — S. 564–567.

Gilboa I., Schmeidler D. Maxmin expected utility with a non-unique prior // Journal of Mathematical Economics. — 1989. — 18, № 2. — P. 141–153.

Tversky A., Kahneman D. Advances in prospect theory: cumulative representation of uncertainty // Journal of Risk and Uncertainty. — 1992. — 5, № 4. — P. 297–323.

Maccheroni F., Marinacci M., Rustichini A. Ambiguity aversion, robustness, and the variational representation of preferences // Econometrica. — 2006. — 74, № 6. — P. 1447–1498.

Mikhalevich V.M. Zadachi prinyatiya resheniya s denezhnymi dokhodami (poteryami) pri sochetanii printsipov garantirovannogo i nailuchshego rezul’tatov // Kibernetika i sistemnyy analiz. — 2012. — № 6. — S. 85–95.

Kolmogorov А.N. O logicheskikh osnovakh teorii veroyatnostey // Teoriya veroyatnostey i matematicheskaya statistika. — M.: Nauka, 1986. — S. 467–471.

Ivanenko V.I., Labkovskiy V.А. Odna model’ nestokhasticheskoy sluchaynosti // DАN SSSR. — 1990. — 310, № 5. — S. 1059–1062.

Ivanenko V.I., Labkovskii V.A. A class of criterion-choosing rules // Soviet Physics Doklady. — 1986. — 31, № 3. — P. 204–205.

Ivanenko V.I., Labkovskii V.A. On the functional dependence between the available information and the chosen optimality principle // Stochastic Optimization, Lecture Notes in Control and Information Sciences. — Springer–Verlag, 1986. — P. 388–392.

Ivanenko V.I., Kuts А.V., Pasichnichenko I.А. K parametrizatsii lotereynoy modeli neparametricheskoy situatsii prinyatiya resheniy // Kibernetika i sistemnyy analiz. — 2014. — № 2. — S. 83–88.

Edvards R. Funktsional’nyy analiz: Per. s angl. — M.: Mir, 1969. — 1071 s.

Danford N., SHvarts Dzh.T. Lineynyye operatory (obshchaya teoriya): Per. s angl. — M.: Izd-vo IL, 1962. — 896 s.

Ivanenko V.I., Labkovskiy V.А. Problema neopredelennosti v zadachakh prinyatiya resheniy — K.: Nauk. dumka, 1990. — 136 s.

Fishbern P. Teoriya poleznosti dlya prinyatiya resheniy: Per. s angl. — M.: Nauka, 1978. — 352 s.

De Groot M. Optimal’nyye statisticheskiye resheniya: Per. s angl. — M.: Mir, 1975. — 491 s.

Published

2015-06-22

Issue

Section

Decision making and control in economic, technical, ecological and social systems