首页|Generalized open-loop Nash equilibria in linear-quadratic difference games with coupled-affine inequality constraints
Generalized open-loop Nash equilibria in linear-quadratic difference games with coupled-affine inequality constraints
Generalized open-loop Nash equilibria in linear-quadratic difference games with coupled-affine inequality constraints
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Puduru Viswanadha Reddy,Partha Sarathi Mohapatra.Generalized open-loop Nash equilibria in linear-quadratic difference games with coupled-affine inequality constraints[EB/OL].(2025-10-03)[2025-10-10].https://arxiv.org/abs/2310.01895.点此复制
In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence of generalized open-loop Nash equilibria in this game class lead to two strongly coupled discrete-time linear complementarity systems. Subsequently, we derive sufficient conditions by establishing an equivalence between the solutions of these systems and convexity of the players' objective functions. These conditions are then reformulated as a solution to a linear complementarity problem, providing a numerical method to compute these equilibria. We illustrate our results using a network flow game with constraints.
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