Distributed Solutions of Convex-Concave Games on Networks
Yingying Xiao, Xiaodong Hou, Jianghai Hu · 2019
In this paper, we study the convex-concave games played by two teams on a network. Each node of the network has local variables from both teams and a local payoff function that is convex in the variables of one team and concave in the variables of the other. The local payoff function may depend on the variables from its neighbors as well. The goal is to find a saddle point of the sum of all local payoff functions. Using the saddle differential operator, we convert the problem to a fixed point problem and propose a synchronous distributed algorithm that can efficiently find the saddle points through a proper splitting of the payoff functions. Its randomized, asynchronous implementation is also discussed. Numerical examples are provided to illustrate the proposed algorithms.