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1 1998

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Memoryless equilibrium strategies in multilevel decision processes of discrete-time descriptor systems

Xu H., Mizukami K., Kobara M.

Control and Cybernetics

1998

Vol. 27, no 1

81-103

Applying a general theorem developed by Basar (1981), providing a set of sufficient conditions for a triple of strategies to be in hierarchical equilibrium, to games in normal (strategic) form, we study three-player Stackelberg games for linear quadratic discrete-time descriptor systems with three levels of hierarchy in decision making. We derive explicitly sufficient conditions for the existence of the memoryless hierarchical equilibrium strategies for the player (called P[sub 1]) at the top of the hierarchy, and for the player (called P[sub 2]) at the second level of the hierarchy. Since the resulting hierarchical equilibrium strategies do not depend on the memory information, P[sub 1]'s original optimal team cost remains the tight (attainable) lower bound for P[sub 1]'s cost function no matter whether the players at the lower levels of hierarchy act or not at the last two (or one) stages. Moreover, the resulting strategies have the advantages of simpler structure and higher credibility. A numerical example is solved to illustrate the validity of the results.