Explicit Solutions of Linear Quadratic Differential Games

A. Bensoussan ()
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A. Bensoussan: University of Texas at Dallas School of Management

Chapter Chapter 2 in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, 2006, pp 19-34 from Springer

Abstract: 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.

Keywords: Nash Equilibrium; Maximum Principle; Stationary Case; Explicit Solution; Riccati Equation (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/0-387-33815-2_2

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