Accelerated Nash equilibrium seeking algorithm with local memory for two-subnetwork zero-sum games

This paper focuses on the distributed Nash equilibrium seeking problem for two-subnetwork zero-sum games. We first utilize the local memory information to design an accelerated algorithm in a distributed manner for the two-subnetwork zero-sum game. Then, we present a sufficient condition for the exponential convergence of the proposed algorithm with local memory, which can ensure the agents’ states converge exponentially to the unique Nash equilibrium. One of the advantages of the proposed algorithm is that the communication requirements are weaker than those of the existing ones. Finally, we use numerical experiments to demonstrate that the convergence speed of the proposed algorithm can be accelerated if the appropriate memory factor is selected and is faster than that of the existing ones. • Based on the gradient tracking method and local memory, we design a distributed discrete-time fixed-stepsize Nash equilibrium seeking algorithm for the two-subnetwork zero-sum game. • We weaken the requirement for the communication compared to the existing distributed discrete-time algorithms for the two-subnetwork zero-sum game. • The convergence speed of proposed algorithm is faster than that of the existing distributed discrete-time algorithms for the two-subnetwork zero-sum game.