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Two-person game with nash equilibrium in optimal control problems

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Abstract

A two-person game with a Nash equilibrium is formulated for optimal control problems with a free right end and a linear differential system. The game is reduced to the calculation of a fixed point of an extremal mapping, which in turn is reduced to a variational inequality with linear constraints generated by systems of linear differential controllable processes. An extra-gradient iterative method is proposed for calculating the Nash equilibrium of the dynamic game. The convergence of the method is proved.

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  1. Computing Center of Russian Academy of Sciences, Vavilov str., 40, 119333, Moscow, Russia

    Anatoly Antipin

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  1. Anatoly Antipin
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Antipin, A. Two-person game with nash equilibrium in optimal control problems. Optim Lett 6, 1349–1378 (2012). https://doi.org/10.1007/s11590-011-0440-x

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  • DOI: https://doi.org/10.1007/s11590-011-0440-x

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