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Mixed strategies in vector optimization and Germeier’s convolution. (English. Russian original) Zbl 1430.90513

J. Comput. Syst. Sci. Int. 58, No. 4, 601-615 (2019); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2019, No. 4, 106-120 (2019).
Summary: The simplest two-criteria examples of a vector optimization problem and a zero-sum game are considered to study the adequacy of using mixed strategies if the linear convolution is replaced by the Germeier’s convolution (the inverse logical convolution) for parametrizing the set of optimal solutions or values of the game and also for estimating the payoffs of all participants. It is shown that the linear convolution yields different results in a comparison with the averaged inverse logical convolution. The issues of stochastic vector optimization and various conceptual formalizations for the value of multi-criteria mixed strategies games are discussed.

MSC:

90C29 Multi-objective and goal programming
91A23 Differential games (aspects of game theory)
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