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.


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