Distributed Nash equilibrium seeking of aggregative games under networked attacks

This paper investigates the distributed Nash equilibrium seeking problem of aggregative games in the presence of networked attacks. A switched algorithm with the fast estimate dynamics is proposed to explore the effect of attacks on seeking a Nash equilibrium. To guarantee the convergence of this algorithm, such a switched strategy is modeled as a hybrid system by using the hybrid automaton and time-ratio conditions. Then, by constructing an appropriate Lyapunov function, we can prove that the hybrid dynamical system is exponentially stable and the Nash equilibrium can be achieved exponentially though the communication network is affected by attacks. Finally, a Nash-Cournot game is provided to verify the main results.