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A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games

Engwerda,Jacob
Abstract
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformulate the Riccati equations into an extended eigenvalue-eigenvector problem for a specific parametrized matrix U ∈ ℝ2N ×2N. Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.
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Date
2015
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Tilburg University Research Output Collection
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Keywords
Riccati equations, differential games, eigenvalues and eigenfunctions, feedback, linear systems, matrix algebra
Citation
Engwerda, J 2015, 'A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games', IEEE Transactions on Automatic Control, vol. 60, no. 11, pp. 3101-3106. https://doi.org/10.1109/TAC.2015.2411914
URI
https://hdl.handle.net/20.500.14602/64609
License
info:eu-repo/semantics/closedAccess
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