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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 2, Pages 359-366

Analytic solution of Riccati equations occurring in open-loop Nash multiplayer differential games

Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E.T.S.I.I., P.O. Box 22.012, Valencia, Spain

Received 2 January 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we present explicit analytic solutions of coupled Riccati matrix differential systems appearing in open-loop Nash games. Two different cases are considered. Firstly, by means of appropriate algebraic transformations the problem is decoupled so that an explicit solution of the problem is available. The second is based on the existence of a solution of a rectangular Riccati type algebraic matrix equation associated with the problem.