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Differential games of evasion with many pursuers. (English) Zbl 0679.90110
Summary: We extend the method of W. Rzymowski [“Method of construction of the evasion strategy for differential games with many pursuers”, Diss. Math. 247 (1986; Zbl 0597.90106)] to the general case, i.e., to games governed by an equation of the form \(z'=f(t,z,u,v)\), where the terminal set is a finite union of linear subspaces of the state space. We prove a theorem providing a new sufficient condition for avoidance of many pursuers that is more general than previous ones. To apply this method to such a general case, we introduce a new strategy for the evader; however, use of similar strategies from Rzymowski is also possible. After obtaining this result, we find a similar condition concerning games governed by many differential equations. Last we consider games described by kth order differential inclusions. For such games (with many pursuers) we give a new sufficient condition for “evasion along each trajectory of a certain set.”

MSC:
91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)
91A99 Game theory
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