# State-Feedback Zero-Sum Differential Games

# State-Feedback Zero-Sum Differential Games

This chapter focuses on the computation of the saddle-point equilibrium of a zero-sum continuous time dynamic game in a state-feedback policy. It begins by considering the solution for two-player zero sum dynamic games in continuous time, assuming a finite horizon integral cost that Player 1 wants to minimize and Player 2 wants to maximize, and taking into account a state feedback information structure. Continuous time dynamic programming can also be used to construct saddle-point equilibria in state-feedback policies. The discussion then turns to continuous time linear quadratic dynamic games and the use of dynamic programming to construct a saddle-point equilibrium in a state-feedback policy for a two-player zero sum differential game with variable termination time. The chapter also describes pursuit-evasion games before concluding with a practice exercise and the corresponding solution.

*Keywords:*
saddle-point equilibrium, continuous time dynamic, state-feedback policy, zero sum dynamic, state feedback information structure, continuous time dynamic programming, continuous time linear quadratic dynamic, zero sum differential, variable termination time, pursuit-evasion game

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