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Characterization of Feedback Nash Equilibrium for Differential Games

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 12))

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Abstract

We investigate the set of Nash equilibrium payoffs for two-person differential games. The main result of the paper is the characterization of the set of Nash equilibrium payoffs in terms of nonsmooth analysis. In addition, we obtain the sufficient conditions for a couple of continuous functions to provide a Nash equilibrium. This result generalizes the method of the system of Hamilton–Jacobi equations.

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Acknowledgements

This work was supported by the Russian Foundation for Basic Research (Grant No. 09-01-00436-a), a grant of the president of the Russian Federation (Project MK-7320.2010.1), and the Russian Academy of Sciences Presidium Programs of Fundamental Research, Mathematical Theory of Control.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics UrB RAS, S. Kovalevskaya Street 16, GSP-384, Ekaterinburg, 620990, Russia

    Yurii Averboukh

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  1. Yurii Averboukh
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Correspondence to Yurii Averboukh .

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Editors and Affiliations

  1. , CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Pierre Cardaliaguet

  2. Wilfrid Laurier University, University Ave W 75, Waterloo, N2L 3C5, Ontario, Canada

    Ross Cressman

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Averboukh, Y. (2013). Characterization of Feedback Nash Equilibrium for Differential Games. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_6

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