Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note  consider linear stationary feedback Nash equilibria of the scalar linear-quadratic differential game. The planning horizon considered is assumed to be infinite.  present both necessary and sufficient conditions on the system parameters for the existence of a unique solution of the associated algebraic Riccati equations (ARE) that stabilizes the closed-loop system. For the case of more solutions, singleton-valued refinements of the equilibrium concept are studied.
['Jacob Engwerda']
I am writing a research paper on a idea Feedback Nash equilibria in the scalar infinite horizon LQ-Game
[{"from": "human", "value": "I am writing a research paper on a idea Feedback Nash equilibria in the scalar infinite horizon LQ-Game"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note  consider linear stationary feedback Nash equilibria of the scalar linear-quadratic differential game. The planning horizon considered is assumed to be infinite.  present both necessary and sufficient conditions on the system parameters for the existence of a unique solution of the associated algebraic Riccati equations (ARE) that stabilizes the closed-loop system. For the case of more solutions, singleton-valued refinements of the equilibrium concept are studied."}]