Journal of Optimization Theory and Applications

, Volume 35, Issue 3, pp 443–464 | Cite as

Stackelberg strategies in linear-quadratic stochastic differential games

  • A. Bagchi
  • T. Başar
Contributed Papers


This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.

Key Words

Stochastic differential games Stackelberg solution linear-quadratic games nonzero-sum games 


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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • A. Bagchi
    • 1
  • T. Başar
    • 2
  1. 1.Department of Applied MathematicsTwente University of TechnologyEnschedeHolland
  2. 2.Applied Mathematics DivisionMarmara Scientific and Industrial Research InstituteGebze, KocaeliTurkey

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