Distributed Nash Equilibrium Seeking via the Alternating Direction Method of Multipliers
It provides a relatively fast distributed method for Nash equilibrium seeking in multi-agent systems, but the contribution appears incremental as it adapts existing ADMM techniques.
This paper develops a distributed algorithm based on inexact ADMM to find Nash equilibria in multi-player games where players only know their own cost functions and all action spaces. The algorithm converges to a Nash equilibrium under mild assumptions, with convergence rate demonstrated via simulations.
In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within the framework of inexact-ADMM. It requires a communication graph for the information exchange between the players as well as a few mild assumptions on cost functions. The convergence proof of the algorithm to a Nash equilibrium of the game is then provided. Moreover, the convergence rate is investigated via simulations.