A new approach to optimal solutions of noncooperative games: accounting for Savage-Niehans risk

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, Department of Optimal Control, Leninskiye Gory, GSP-1, Moscow, 119991, Russia
^b Federal State Budgetary Institution of Science Central Economic and Mathematical Institute of the Russian Academy of Sciences (CEMI RAS), Nakhimovskii prosp., 47, Moscow, 117418, Russia

Abstract: The novelty of the approach presented below is that each person in a conflict (player) seeks not only to increase his payoff but also to reduce his risk, taking into account a possible realization of any uncertainty from a given admissible set. A new concept, the so-called strongly-guaranteed Nash equilibrium in payoffs and risks, is introduced and its existence in mixed strategies is proved under standard assumptions of the theory of noncooperative games, i.e., compactness and convexity of the sets of players’ strategies and continuity of the payoff functions.

Keywords: Savage–Niehans risk, minimax regret, uncertainties, noncooperative game, optimal solution

UDC: 517.577.1

MSC: 91A10

Language: English