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Optimization Letters

, Volume 13, Issue 8, pp 1913–1925 | Cite as

Program strategies for a dynamic game in the space of measures

  • Nikolay PogodaevEmail author
Original Paper
  • 99 Downloads

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.

Keywords

Continuity equation Liouville equation Dynamic game Program strategies 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsYekaterinburgRussia
  2. 2.Matrosov Institute for System Dynamics and Control TheoryIrkutskRussia

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