On the Characterization of Local Nash Equilibria in Continuous Games

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 equi...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2016-08, Vol.61 (8), p.2301-2307
Main Authors: Ratliff, Lillian J., Burden, Samuel A., Sastry, S. Shankar
Format: Article
Language:English
Subjects:
Automatic control
Cost function
Game theory
Games
Manganese
Manifolds
Nash equilibrium
optimization
Programming
Strategy
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Summary: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 isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2583518