# American Institute of Mathematical Sciences

2013, 3(1): 95-108. doi: 10.3934/naco.2013.3.95

 1 Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, TX 75080-3021, United States, United States, United States

Received  October 2011 Revised  November 2012 Published  January 2013

This paper is concerned with open-loop Stackelberg equilibria of two-player linear-quadratic differential games with mixed leadership. We prove that, under some appropriate assumptions on the coefficients, there exists a unique Stackelberg solution to such a differential game. Moreover, by means of the close interrelationship between the Riccati equations and the set of equations satisfied by the optimal open-loop control, we provide sufficient conditions to guarantee the existence and uniqueness of solutions to the associated Riccati equations with mixed-boundary conditions. As a result, the players' open-loop strategies can be represented in terms of the system state.
Citation: Alain Bensoussan, Shaokuan Chen, Suresh P. Sethi. Linear quadratic differential games with mixed leadership: The open-loop solution. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 95-108. doi: 10.3934/naco.2013.3.95
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