Open‐loop equilibrium seeking in two‐agent noncooperative linear‐quadratic dynamic game with asymmetric horizon length

Abstract

This article proposes an iterative‐based algorithm for open‐loop equilibrium seeking in a two‐agent noncooperative dynamic game. The finite‐horizon dynamic games handled in almost all existing articles assume the common prediction horizon length. From the viewpoint of divergence and differences in personal values, it is socially rational to solve the equilibrium of the games with asymmetric prediction horizon length. We thus propose an open‐loop equilibrium‐seeking algorithm without the private knowledge of the other agent's horizon information through a receding‐horizon linear‐quadratic game. Our proposed algorithm is based on iterative optimization. Each agent obtains its own best response control strategy while estimating the other agent's state feedback gain from the state information and guaranteeing the stability of the whole system. We also discuss the performance of the proposed equilibrium‐seeking algorithm through numerical examples.