Generalized Nash Equilibrium Problem by the Alternating Direction Method of Multipliers
For researchers in distributed optimization and game theory, this work provides a convergent algorithm for GNE with private constraints, though it is incremental as it applies ADMM to a known problem setting.
The paper addresses the generalized Nash equilibrium problem in networked games with private constraints, proposing an algorithm based on inexact ADMM that converges under mild assumptions. Simulations on wireless ad-hoc networks demonstrate its effectiveness.
In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear equality constraint that is coupled through decisions of the other players. We consider that each player has his own private constraint and it has not to be shared with the other players. This general case also embodies the one with shared constraints between players and it can be also simply extended to the case with inequality constraints. Since the players don't have access to other players' actions, they need to exchange estimates of others' actions and a local copy of the Lagrangian multiplier with their neighbors over a connected communication graph. We develop a relatively fast algorithm by reformulating the conservative GNE problem within the framework of inexact-ADMM. The convergence of the algorithm is guaranteed under a few mild assumptions on cost functions. Finally, the algorithm is simulated for a wireless ad-hoc network.