Abstract
The paper formalizes and investigates a concept of new solving the differential positional linear-quadratic non-cooperative four-person game under uncertainty. The given solution unites the well-known concepts of optimality of non-cooperative games theory (Nash equilibrium and equilibrium of threats and counterthreats). The account of uncertain factors is made by means of "analog of a vector saddle point". The existence conditions are established and the explicit form of such solution is found.
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