A new approach to guaranteed solutions of multicriteria choice problems: Pareto consideration of Savage-Niehans risk and outcomes

V. I. Zhukovskii^a, L. V. Zhukovskaya^b, Yu. S. Mukhina<sup>a

a</sup> Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Federal State Budgetary Institution of Science Central Economic and Mathematical Institute of the Russian Academy of Sciences

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.

Keywords: Savage–Niehans risk, minimax regret, uncertainties, multicriteria choice, Pareto consideration.

UDC: 519.810

MSC: 91.830

Language: English