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The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations


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  • Engwerda, J.C.

    (Tilburg University, Center for Economic Research)


In this paper we analyse the set of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar N-player linear-quadratic differential game. We show that in general there exist maximal 2N - 1 solutions of the (ARE) that give rise to a Nash equilibrium. In particular we analyse the number of equilibria as a function of the state-feedback parameter and present both necessary and sufficient conditions for existence of a unique solution of the (ARE). Furthermore, we derive conditions under which the set of state-feedback parameters for which there is a unique solution grows with the number of players in the game.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-90.

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Date of creation: 1999
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Handle: RePEc:dgr:kubcen:199990

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Keywords: Linear quadratic games; feedback Nash equilibrium; solvability conditions; Riccati equations;

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  1. 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.
  2. Engwerda, J.C. & Salmah, Y., 2010. "Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games," Discussion Paper 2010-79, Tilburg University, Center for Economic Research.
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Cited by:
  1. Acocella Nicola & Di Bartolomeo Giovanni, 2007. "Towards a new theory of economic policy: Continuity and innovation," wp.comunite 0020, Department of Communication, University of Teramo.
  2. Engwerda, J.C., 2004. "A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142827, Tilburg University.
  3. Tamer Ba┼čar & Quanyan Zhu, 2011. "Prices of Anarchy, Information, and Cooperation in Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 50-73, March.
  4. Engwerda, J.C., 2013. "A Numerical Algorithm to find All Scalar Feedback Nash Equilibria," Discussion Paper 2013-050, Tilburg University, Center for Economic Research.


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