A distributed proximal-point algorithm for nash equilibrium seeking in generalized potential games with linearly coupled cost functions

We address the generalized Nash equilibrium seeking problem for a population of noncooperative agents playing potential games with linear coupling constraints over a communication network. We consider a class of generalized potential games where the coupling in the cost functions of the agents is linear, i.e., J{i}(x{i}, x{-i}): =f{i}(x{i})+ ell{i}(x{-i}){ top}x{i} where ell{i} is linear. By exploiting this special structure, we design a distributed algorithm with convergence guarantee under mild assumptions, i.e., (non-strict) monotonicity of the pseudo-subdifferential mapping. The potential of the proposed algorithm is shown via numerical simulations on a networked Nash Cournot game, where we observe faster convergence with respect to standard projected pseudo-gradient algorithms.