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 trajectory and the other player's cost. To mitigate these effects, we construct a compensation law for the influenced player by augmenting the nominal game with the measurable deviation dynamics. The resulting policy is shown to be optimal within a causal affine policy class, and, for sufficiently small deviations, it locally outperforms the uncompensated equilibrium-derived feedback. Rigorous analysis and proofs are provided, and the effectiveness of the proposed approach is demonstrated through a representative numerical example.

翻译：博弈论方法与纳什均衡已在众多工程领域得到广泛应用。然而，实际应用中存在的扰动、时滞和执行器限制等挑战，可能阻碍纳什均衡策略的精确执行。本文研究在一个双参与者有限时域线性二次非零和博弈中，此类执行缺陷对博弈轨迹与参与者成本的影响。具体而言，我们分析了单参与者在每个阶段存在可测量或可估计的微小偏差时，如何影响状态轨迹及另一参与者的成本。为减轻这些影响，我们通过将可测偏差动态引入标称博弈，为受影响的参与者构建了一种补偿律。结果表明，所得策略在因果仿射策略类中是最优的，并且对于足够小的偏差，其局部性能优于未补偿的均衡反馈策略。本文提供了严格的理论分析与证明，并通过典型数值算例验证了所提方法的有效性。