The zero-sum discrete-time feedback linear quadratic dynamic game: From two-player case to multi-player case

Musthofa, Muhammad Wakhid
Engwerda, Jacob

Bulletin of Applied Mathematics and Mathematics Education
Vol. 4 No. 1 (2024)

The two-person zero-sum discrete-time feedback linear quadratic dynamic game is considered. A method that provides a saddle-point for the zero-sum discrete dynamic game is developed to derive a necessary and sufficient condition under which the game has a feedback saddle-point solution. Existence solutions, which are described in terms of a sequence of nonnegative definite algebraic Riccati matrices, are constructed. Next, a generalization of such a game to a multi-player case is studied. Using the results in a two-person case, the characterization of a feedback saddle-point solution for the multi-player game is derived.