  To optimally select a generalized Nash equilibrium, in this paper, we propose
a semi-decentralized algorithm based on a double-layer Tikhonov regularization
method. Technically, we extend the Tikhonov method for equilibrium selection in
non-generalized games to the generalized case by coupling it with the
preconditioned forward-backward splitting, which guarantees linear convergence
to the solutions of the inner layer problem and allows for a semi-decentralized
implementation. We then establish a conceptual connection and draw a comparison
between the proposed algorithm and the hybrid steepest descent method, the
other known distributed framework for solving the selection problem.
