×

On Nash equilibria for noncooperative games governed by the Burgers equation. (English) Zbl 1127.91012

The author develops a theoritical solution scheme of non-cooperative games governed by Burgers equation using the idea of Nash equilibria. A number of theorems were preseted for theoretical stability and convergence. There is no experimental validation of the proposed theory.

MSC:

91A23 Differential games (aspects of game theory)
49N70 Differential games and control
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ramos, A. M., Glowinski, R., and Periaux, J., Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach, Journal of Optimization Theory and Applications, Vol. 112, pp. 499–516, 2002. · Zbl 1027.49020 · doi:10.1023/A:1017907930931
[2] Roubívcek, T., On Noncooperative Nonlinear Differential Games, Kybernetika,Vol. 35, pp. 487–498, 1999. · Zbl 1274.91073
[3] Roubívcek, T., Noncooperative Games with Elliptic Systems, Optimal Control of Partial Differential Equations, Edited by K. H. Hoffmann, G. Leugering, and F. Tröltzsch, Birkhäuser, Basel, Switzerland, pp. 245–255, 1999. · Zbl 0965.91006
[4] Roubívcek, T., Optimization of Steady-State Flow of Incompressible Fluids, Analysis and Optimization of Differential Systems, Edited by V. Barbu, I. Lasiecka, D. Tiba, and C. Varsan, Kluwer Academic Publishers, Boston, Massachusetts pp. 357–368,2003. · Zbl 1038.35079
[5] Gabasov, R., and Kirillova, F., The Qualitative Theory of Optimal Processes, Nauka, Moscow, Russia, 1971; English Translation: Marcel Dekker, New York, NY,1976. · Zbl 0236.49001
[6] Bubák, P., Optimal Control of a Flow Driven by a Thermal Field, Mathematical-Physical Faculty, Charles University, Prague, Czech Republic, MS Thesis, 2003.
[7] Nash, J., Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951. · Zbl 0045.08202 · doi:10.2307/1969529
[8] Nikaido, H., and Isoda, K., Note on Noncooperative Equilibria, Pacific Journal of Mathematics, Vol. 5, pp. 807–815, 1955. · Zbl 0171.40903
[9] Roubívcek, T., Relaxation in Optimization Theory and Variational Calculus, Walter de Gruyter, Berlin, Germany, 1997. · Zbl 0880.49002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.