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A Numerical Algorithm to find All Scalar Feedback Nash Equilibria

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  • Engwerda, J.C.

    (Tilburg University, Center for Economic Research)

Abstract

Abstract: In this note we generalize a numerical algorithm presented in [9] 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 Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-050.

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Date of creation: 2013
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Handle: RePEc:dgr:kubcen:2013050

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Web page: http://center.uvt.nl

Related research

Keywords: linear-quadratic differential games; linear feedback Nash equilibrium; affine systems; numerical solution; Riccati equations;

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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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