Construction of control ensuring equilibrium conditions in a multistep two-person positional game

G. A. Zograbyan, V. Yu. Reshetov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: An analytical approach is suggested for finding a strategy in a conflict situation described by a linear control system. A modified dynamic programming method is examined as applied to a multistep differential game. The method is used to construct a Nash equilibrium solution.

Key words: differential game, Nash equilibrium, conflict situation, multistep game.

UDC: 519.626

MSC: 91A23 (49N70 91A24 93B50)

Received: 28.11.2013

DOI: 10.7868/S0044466914060180

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:6, 931–938

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