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Journal of Automation and Information Sciences

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Journal of Automation and Information Sciences


10 pages

Existence of Hybrid Equilibrium in a Differential Game

Vladislav I. Zhukovskiy
Russian Correspondence Institute of Textile and Light Industry, Moscow, Russia
Victor V. Zolotaryov
Russian Correspondence Institute of Textile and Light Industry, Moscow, Russia

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.