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Program strategies for a dynamic game in the space of measures

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Abstract

The continuity equation describes the transport of a distributed quantity along a vector field. If two independent players affect the vector field we arrive at a game with dynamics given by the continuity equation, or a game in the space of measures. For this game, we discuss a notion of program strategy, provide an existence theorem for the equilibrium, and prove a necessary equilibrium condition.

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Acknowledgements

The work was supported by the Russian Science Foundation, Grant No. 17-11-01093.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Kovalevskay Str., 16, Yekaterinburg, Russia, 620990

    Nikolay Pogodaev

  2. Matrosov Institute for System Dynamics and Control Theory, Lermontov Str., 134, Irkutsk, Russia, 664033

    Nikolay Pogodaev

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  1. Nikolay Pogodaev
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Correspondence to Nikolay Pogodaev.

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Pogodaev, N. Program strategies for a dynamic game in the space of measures. Optim Lett 13, 1913–1925 (2019). https://doi.org/10.1007/s11590-018-1318-y

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  • DOI: https://doi.org/10.1007/s11590-018-1318-y

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