📝 SummarXiv

Abstract

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash equilibrium strategies. This work investigates the impact of such implementation imperfections on game trajectories and players' costs in the context of a two-player finite-horizon linear quadratic (LQ) nonzero-sum game. Specifically, we analyze how small deviations by one player, measured or estimated at each stage, affect the state and cost function of the other player. To mitigate these effects, we propose an adjusted control policy that optimally compensates for the deviations under the stated information structure and can, under certain conditions, exploit them to improve performance. Rigorous mathematical analysis and proofs are provided, and the effectiveness of the proposed method is demonstrated through a representative numerical example.