  In this paper, a multi-cluster game with high-order players is investigated.
Different from the well-known multi-cluster games, the dynamics of players are
taken into account in our problem. Due to the high-order dynamics of players,
existing algorithms for multi-cluster games cannot solve the problem. For
purpose of seeking the Nash equilibrium of the game, we design a distributed
algorithm based on gradient descent and state feedback, where a distributed
estimator is embedded for the players to estimate the decisions of other
players. Furthermore, we analyze the exponential convergence of the algorithm
via variational analysis and Lyapunov stability theory. Finally, a numerical
simulation verifies the effectiveness of our method.
