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

To optimally select a generalized Nash equilibrium, in this paper, we consider a semi-decentralized algorithm based on a double-layer Tikhonov regularization algorithm. Technically, we extend the Tikhonov method for equilibrium selection to generalized games. Next, we couple such an algorithm with the preconditioned forward-backward splitting, which guarantees linear convergence to a solution of the inner layer problem and allows for a semi-decentralized implementation. We then establish a conceptual connection and draw a comparison between the considered algorithm and the hybrid steepest descent method, the other known distributed approach for solving the equilibrium selection problem.