On the Characterization of Local Nash Equilibria in Continuous Games

@article{Ratliff2016OnTC,
  title={On the Characterization of Local Nash Equilibria in Continuous Games},
  author={Lillian J. Ratliff and Samuel Burden and S. Shankar Sastry},
  journal={IEEE Transactions on Automatic Control},
  year={2016},
  volume={61},
  pages={2301-2307}
}
We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria. Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are… CONTINUE READING
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