Linear quadratic differential games with mixed leadership: The open-loop solution

Alain  Bensoussan; Shaokuan Chen; Suresh P. Sethi

doi:10.3934/naco.2013.3.95

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2013, Volume 3, Issue 1: 95-108. Doi: 10.3934/naco.2013.3.95

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Linear quadratic differential games with mixed leadership: The open-loop solution

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

Received: September 30, 2011

Revised: October 31, 2012

Published: December 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 91A10, 91A23; Secondary: 34K10.

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