Discrete Mathematics and Mathematical Cybernetics

Solution of the coalition game in the program strategy under uncertainty

E. D. Nasonova

Balashov Institute (Branch) of the Saratov National Research State University, Balashov, Russian Federation

Abstract: The abstract game models of conflict are widely used in practice in solving problems of management systems of different nature. The paper constructs a mathematical model of differential game of two coalitions with uncertainty in program strategies, considers antagonistic interaction between coalitions, defines the solutions using the principle of a guaranteed result. Application of the method of penalty functions has transformed the original maxmin problem in the related sets to the task for maximum. The paper proves the existence theorem for solutions to problems with penalties, an estimate of the error, matching conditions penalty constants and optionally-necessary condition of optimality.

Keywords: coalition game, the uncertainty, the method of penalties.

UDC: 517.977

Received: 22.10.2015

DOI: 10.14529/cmse160205

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