Distributed convergence to nash equilibrium of antagonistic optimization networks

In this paper, we propose a distributed subgradient-based algorithm for a network consisting of two subnetworks to solve the antagonistic optimization problem. The two subnetworks have the same sum objective function, where one wants to minimize it and the other one wants to maximize it. Then the network is engaged in a zero-sum game scenario. We show that the network can achieve a Nash equilibrium by the proposed algorithm for weight-balanced digraphs under mild connectivity and stepsize conditions.