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.
This article investigates the generalized Nash equilibrium (GNE) seeking for the game with equality constraints. Each player cannot directly access all the other player's actions and the gradients of all players' payoff functions are unknown. In these scenarios, an interesting question is under what distributed algorithm the GNE can be found. To address such games, we first design a two‐time‐scale distributed algorithm based on the extremum seeking method and consensus protocol. Then, by utilizing singular perturbation techniques and Lyapunov robust analysis, we show that the players' decisions can be regulated to an arbitrarily small neighborhood of the GNE. Moreover, we further consider the ideal case in which the gradients are known. In this case, the proposed strategy can be degenerated to a gradient‐based algorithm and the players' decisions exponentially converge to the GNE. Finally, two examples along with simulation results are used to illustrate the effectiveness of the proposed algorithms.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.