PDFAbstract: We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The accelerated Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in [6], where the convergence properties are established. In addition, the Lyapunov iterative method to compute the Nash equilibrium point is presented in [7] (5th International Conference Applied and Computational Mathematics, WSEAS Conference at Mallorca, 2016). Based on these two methods we derive a new one - the accelerated Lyapunov method. Moreover, the convergence properties are proved. The performances of the proposed algorithm are illustrated on some numerical examples.
Keywords: feedback Nash equilibrium, generalized Riccati equation, stabilizing solution, nonnegative solution REFERENCES [1] T. Azevedo-Perdicoulis and G. Jank, Linear Quadratic Nash Games on Positive Linear Systems, European Journal of Control, 11, 2005, 1– 13. [1] T. Azevedo-Perdicoulis and G. Jank, Linear Quadratic Nash Games on Positive Linear Systems, European Journal of Control, 11, 2005, 1– 13. [2] B. Bazar and G. J. Olsder, Dynamic Noncooperative Game Theory, SIAM, (1999). [3] S. Jorgensen, and G. Zaccour, Differential Games in Marketing. International Series in Quantitative Marketing, Kluwer Academic Publisher in 2004. [4] E. Dockner, S. Jorgensen, N. V. Long, G. Sorger, Differential games in economics and management science, Cambridge University Press, (2000). [5] L. Imsland, I. G.Ivanov and S.Kostova, Linear Quadratic Differential Games and Applications, Biomath Communications, 3, 2016, N 2, [6] I. G.Ivanov, L. Imsland and B. C. Bogdanova, Iterative Algorithms for Computing the Feedback Nash Equilibrium Point for Positive Systems, accepted in International Journal of System Science, [7] I. G.Ivanov and N. Netov, The Nash Equilibrium Point in the LQ Game on Positive Systems with Two Players, Mathematical and Computational Methods, 1, 2016, 242–246, [8] L. Metzler, Stability of multiple markets: the Hicks condition, Econometrica, 13(4), 1945, pp. 277–292.
Cite this paper
Ivan G. Ivanov, Nikolay Netov, Vladislav Tanov. (2016) Iteratively Computation the Nash Equilibrium Points in the Two-Player Positive Games. International Journal of Mathematical and Computational Methods, 1 , 378-381
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