LANA: An ADMM-like Nash equilibrium seeking algorithm in decentralized environment

We introduce a linearized alternating direction method of multipliers (ADMM)-like Nash equilibrium seeking algorithm (LANA) for a class of non-cooperative games over generally connected networks. This model differs from conventional settings because the communication graph is not necessarily the same as the players' objective dependency network and thus players have to deal with incomplete information issues. To solve this game theoretic problem, the introduced algorithm involves every player performing gradient (projection) play to minimize his own objective selfishly while sharing, retrieving, and combining information locally among his network neighborhood. Convergence guarantees are provided for the algorithm. We further extend the introduced algorithm to asynchronous updates and find it works well. Numerical experiments verify the viability of the algorithms.