Abstract
A method to solve the coupled Riccati type equations occuring in discrete-time linear-quadratic open-loop Nash games is presented. Under the assumption that the state weighting matrices appearing in the players’ cost functions are proportional to each other, it is shown that the matrix characterizing the necessary conditions to be satisfied by an open-loop Nash strategy has a special spectrum. This property is then exploited to obtain a nonrecursive solution for the coupled Riccati equations. An example is given to illustrate the proposed method where algebraic manipulation languages are shown to be quite useful to invert time-dependent matrices.
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