Abstract
The theory of linear quadratic differential games is in principle known. An excellent reference for management and economics applications is Dockner et al. (2000). We review here the results, showing that in useful simple cases, explicit solutions are available. This treatment is not included in the previous reference and seems to be original. In non-stationary cases, explicit solutions are not available, we prove the existence of solutions of coupled Riccati equations, which provide a complete solution of the Nash equilibrium problem.
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References
E. Dockner, S. Jøgensen, N. van Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, 2000.
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© 2006 Springer Science+Business Media, LLC
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Bensoussan, A. (2006). Explicit Solutions of Linear Quadratic Differential Games. In: Yan, H., Yin, G., Zhang, Q. (eds) Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems. International Series in Operations Research & Management Science, vol 94. Springer, Boston, MA . https://doi.org/10.1007/0-387-33815-2_2
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DOI: https://doi.org/10.1007/0-387-33815-2_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-33770-8
Online ISBN: 978-0-387-33815-6
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