On the optimal selection of generalized Nash equilibria in linearly coupled aggregative games

Monotone aggregative games may admit multiple (variational) generalized Nash equilibria, yet currently there is no algorithm able to provide an a-priori characterization of the equilibrium solution actually computed. In this paper, we formulate for the first time the problem of selecting a specific variational equilibrium that is optimal with respect to a given objective function. We then propose a semi-decentralized algorithm for optimal equilibrium selection in linearly coupled aggregative games and prove its convergence.