A Numerical Algorithm to find All Scalar Feedback Nash Equilibria
AbstractAbstract: In this note we generalize a numerical algorithm presented in  to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on calculating the positive roots of a polynomial matrix.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-050.
Date of creation: 2013
Date of revision:
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Web page: http://center.uvt.nl
linear-quadratic differential games; linear feedback Nash equilibrium; affine systems; numerical solution; Riccati equations;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-09-26 (All new papers)
- NEP-CMP-2013-09-26 (Computational Economics)
- NEP-GTH-2013-09-26 (Game Theory)
- NEP-HPE-2013-09-26 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Engwerda, J.C., 2000.
"The solution set of the N-player scalar feedback Nash algebraic Riccati equations,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-85060, Tilburg University.
- Engwerda, J.C., 1999. "The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations," Discussion Paper 1999-90, Tilburg University, Center for Economic Research.
- Broek, W.A. van den & Engwerda, J.C. & Schumacher, J.M., 2003. "Robust equilibria in indefinite linear-quadratic differential games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123066, Tilburg University.
- Jacob Engwerda, 2007.
"Algorithms for computing Nash equilibria in deterministic LQ games,"
Computational Management Science,
Springer, vol. 4(2), pages 113-140, April.
- Engwerda, J.C., 2007. "Algorithms for computing Nash equilibria in deterministic LQ games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-332520, Tilburg University.
- Engwerda, J.C., 2006. "Algorithms for Computing Nash Equilibria in Deterministic LQ Games," Discussion Paper 2006-109, Tilburg University, Center for Economic Research.
- Engwerda, J.C., 2000. "Feedback Nash equilibria in the scalar infinite horizon LQ-Game," Open Access publications from Tilburg University urn:nbn:nl:ui:12-81029, Tilburg University.
- Engwerda, J.C. & Salmah, Y., 2010. "Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential," Discussion Paper 2010-78, Tilburg University, Center for Economic Research.
- Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, April.
- Weeren, A.J.T.M. & Schumacher, J.M. & Engwerda, J.C., 1994. "Asymptotic analysis of Nash equilibria in nonzero-sum linear-quadratic differential games: The two player case," Research Memorandum 634, Tilburg University, Faculty of Economics and Business Administration.
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