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Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games

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Abstract

We consider a noncooperative game in infinite time horizon, with linear dynamics and exponentially discounted quadratic costs. Assuming that the state space is one-dimensional, we prove that the Nash equilibrium solution in feedback form is stable under nonlinear perturbations. The analysis shows that, in a generic setting, the linear-quadratic game can have either one or infinitely many feedback equilibrium solutions. For each of these, a nearby solution of the perturbed nonlinear game can be constructed.

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Acknowledgments

The authors would like to thank the anonymous referee, whose suggestions and comments helped to improve various aspects of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, State College, PA, USA

    Alberto Bressan

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Khai T. Nguyen

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  1. Alberto Bressan
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  2. Khai T. Nguyen
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Correspondence to Khai T. Nguyen.

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Bressan, A., Nguyen, K.T. Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games. Dyn Games Appl 8, 42–78 (2018). https://doi.org/10.1007/s13235-016-0206-2

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