A Semi-Decentralized Tikhonov-based Algorithm for Optimal Generalized Nash Equilibrium Selection

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.