An ADMM Approach to the Problem of Nash Equilibrium Seeking
Farzad Salehisadaghiani, Wei Shi, Lacra Pavel · arXiv (Cornell University) · 2017
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that the communication graph is not necessarily the same as the players' cost dependency graph, and thus players have incomplete information on the actions of their opponents. We develop a relatively fast algorithm within the framework of inexact-ADMM, based on local information exchange between the players. We prove convergence to a Nash equilibrium for fixed step-sizes and analyze its convergence rate. Numerical simulations illustrate its benefits when compared to a consensus-based gradient type algorithm.