A New Approach To Guaranteed Solutions Of Multicriteria Choice Problems: Pareto Consideration Of Savage–Niehans Risk And Outcomes

Zhukovskaya, Lidia and Zhukovskiy, Vladislav and Mukhina, Julia (2023): A New Approach To Guaranteed Solutions Of Multicriteria Choice Problems: Pareto Consideration Of Savage–Niehans Risk And Outcomes. Published in:

Abstract

This article considers three new approaches to important problems of mathematical game theory and multicriteria choice.The first approach ensures payoff increase with simultaneous risk reduction in the Savage–Niehans sense in multicriteria choice problem and noncooperative games. The second approach allow us to stabilize coalitional structures in cooperative games without side payments under uncertainty. The third approach serves to integrate the selfish Nash equilibrium with the altruistic Berge equilibrium. Note that the investigations involve a special Germeier convolution of criteria and calculation of its saddle point in mixed strategies.

• Item Type: MPRA Paper
• Language: English
• Keywords: Savage–Niehans risk, minimax regret, uncertainties, multicriteria choice, Pareto consideration
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General

References

1. Kapitonenko, V. V. (2000) Financial Mathematics and Its Applications. Moscow: Prior.

2. Kolemaev, V. A. (2002) Mathematical Economics. Moscow: Yuniti.

3. Savage, L. Y. (1954) The Foundation of Statistics. New York: Wiley.

4. Savage, L. Y. (1951) The theory of Statistical Decision. J. American Statistic Assosiation. 46. p. 55–67.

5. NICANS, J. (1951) Zur Preisbildung bei Unterwissen. Zchweizerische Zeitschrift Association. 46 (3). p. 55–67.

6. Germeier, Y. B. (1971) Introduction to Operation Research. Moscow: Nauka.

7. Germeier, Y. B. (1976) Games with Nonopposite Interests. Moscow: Nauka.

8. Muschick, E. and muller, P. (1990) Methods of Technical Decision-Making. Moscow: Mir.

9. Knight, F. H. (2003) Risk, Uncertainty, and Profit. Moscow: Delo.

10. Zhukovskiy, V. I. (2007) Conflicts and Risks. Moscow: Ross. Zaochn. Inst. Tekstil. Legk.Promysh.

11. Zhukovskiy, V. I. (2011) Risks in Conflict Situations. Moscow: URSS.

12. Zhukovskiy, V. I., zhukovskaya, L. V. (2004) Risks in Multicriteria Choice and Conflict Systems under Uncertainty. Moscow: URSS.

13. Wald, A. (1939) Contribution to the Theory of Statistical Estimation and Testing Hypothesis. Annuals Math. Statist.. 10. p. 299–326.

14. Wald, A. (1950) A Statistical Decision Functions. N.Y.: Wiley.

15. Aumann, R. (2007) An Economic Index of Riskiness. Russian Management Journal. 5 (5). p. 3–14.

16. Cherkasov, V. V. (1999) Risk Problems in Management. Moscow: Refa-buk.

17. Shakhov, V. V. (1994) Introduction to Insurance. Economic Aspect. Moscow: Finansi i Statistika.

18. Cheremnykh, Y. N. (2008) Microeconomics: Advance Level. Moscow: Info–M.

19. Tsvetkova, E. V. and arlyukova, I. O. (2002) Risks in Economic Activity. St.–Peterburg: Inst. Vneshneekon. Svyav. Ekon. Prav.

20. Markovits, H. M. (1952) Portfolio Selection. Journal of Finance. 7 (1). p. 77–89.

21. Zhukovskiy, V. I. and kudryavtsev, K. N. (2013) Equilibrating Conflicts under Uncertainty. I. Analog of a Saddle–Point. Mat. Teor. Igr Prilozh.. 5 (1). p. 27–44.

22. Zhukovskiy, V. I. and kudryavtsev, K. N. (2013) Equilibrating Conflicts under Uncertainty.II. Analog of a Maximin. Mat. Teor. Igr Prilozh.. 5 (2). p. 3–45.

23. Dmitruk, A. V (2012) Convex analysis. Elementary introductory course. Moscow: MAKS-PRESS.

24. Zhukovskiy, V. I., Salukvadze, M. E. (1994) The vector-valued maximin. N.Y. etc: Academic Press.

25. Arrow, K. J., Hurwicz, L. and Uzawa, H. (1958) Studies in Linear and Non–linear Programming. Stanford Mathematical Studies in the Social Sciences, Stanford Univ. Press.

26. Karlin, S. (1959) Mathematical Methods and Theory in Games. Programming and Economics, London–Paris: Pergamon Press.

27. Kleimenov, A. F. (1993) Nonantogonistic Positional Differential Games. Yekaterinburg: Nauka.

28. Kolesnik, G. V. (2010) Game Theory. Moscow: Librokom.

29. Kudryavtsev, K. N. and Stabulit, I. S. (2012) Pareto–Guaranteed Equilibrium in 2D Hotelling Duopoly. Vest. Yuzhno–Ural. Gos. Univ. Ser. Mat. Modelir. Programmir.. 14 (40). p. 173–177.

30. Zhukovskiy, V. I., Chikrii, A. A. and Soldatova, N. G. (2014) The Berge Equilibrium in the Conflicts under Uncertainty. Proc. XII All-Russian Meeting on Control Problems (AMCP–114), Moscow: Inst. Probl. Upravlen..8290–8302

31. Zhukovskiy, V. I., Salukvadze, M. E. (2020) The Berge Equilibrium: A Game-Theoretic Framework for Golden Rule of Ethics. Springer.

32. Zhukovskiy, V. I., Salukvadze, M. E. (2021) The Berge Equilibrium: A Game-Theoretic Framework for Golden Rule of Ethics. A Dynamic-Theoretic Framework Based of Berge Equilibrium. N.Y.: CRC Press Taylor and Francis Group