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Universal optimal strategies in positional differential games. (English. Russian original) Zbl 0543.90104

Differ. Equations 19, 1377-1382 (1983); translation from Differ. Uravn. 19, No. 11, 1890-1896 (1983).
In a monograph by N. N. Krasovskij and A. I. Subbotin [”Positional differential games” (1974; Zbl 0298.90067)] a formalization of positional (usual) strategies was proposed and for any fixed initial state the existence of an equilibrium situation for these strategies was proved. A strategy is called universal if it is optimal (i.e. equilibrium) for all initial states in a given region. N. N. Krasovskij [Math. USSR, Sb. 35, 795-822 (1979; Zbl 0439.90114)] introduced a new notion of positional (generalized) strategy and proved the existence of a universal generalized strategy. However, it was an open problem whether there exists a universal strategy. The reviewed paper answers this question in the negative. The paper also contains an approach to another determination of universal strategies.

MSC:

91A23 Differential games (aspects of game theory)
91A99 Game theory
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