Nash equilibrium computation in two-network zero-sum games: An incremental algorithm

摘要

In this paper, the problem of distributed Nash equilibrium computation in two-network zero-sum games is studied. Based on a sequential communication strategy, a novel incremental algorithm is developed to compute a Nash equilibrium. Different from the existing algorithms, the agents in two different subnet-works perform their updates in an asynchronous way, and the square-summable assumption of step sizes adopted in the existing methods is removed in our algorithm. In the convergence analysis of the proposed algorithm, two important relations of the agents' equilibrium estimates are firstly provided based on the properties of projection operator. Then by combining the methods of contradiction and mathematical induction, it is proven that the agents' estimates achieve a Nash equilibrium even without the square-summable requirement of step sizes. Finally, simulations are provided to verify the validity of our method. (C) 2019 Elsevier B.V. All rights reserved.