  In this paper, we investigate the noncooperative games of multi-agent
systems. Different from existing noncooperative games, our formulation involves
the high-order nonlinear dynamics of players, and the communication topologies
among players are weight-unbalanced digraphs. Due to the high-order nonlinear
dynamics and the weight-unbalanced digraphs, existing Nash equilibrium seeking
algorithms cannot solve our problem. In order to seek the Nash equilibrium of
the noncooperative games, we propose two distributed algorithms based on state
feedback and output feedback, respectively. Moreover, we analyze the
convergence of the two algorithms with the help of variational analysis and
Lyapunov stability theory. By the two algorithms, the high-order nonlinear
players exponentially converge to the Nash equilibrium. Finally, two simulation
examples illustrate the effectiveness of the algorithms.
