  We consider a generalized Nash equilibrium problem (GNEP) for a network of
players. Each player tries to minimize a local objective function subject to
some resource constraints where both the objective functions and the resource
constraints depend on other players' decisions. By conducting equivalent
transformations on the local optimization problems and introducing network
Lagrangian, we recast the GNEP into an operator zero-finding problem. An
algorithm is proposed based on the Douglas-Rachford method to distributedly
find a solution. The proposed algorithm requires milder conditions compared to
the existing methods. We prove the convergence of the proposed algorithm to an
exact variational generalized Nash equilibrium under two different sets of
assumptions. Our algorithm is validated numerically through the example of a
Nash-Cournot production game.
