We consider targeted intervention problems in dynamic network and graphon games. First, we study a general dynamic network game in which players interact over a graph and seek to maximize their heterogeneous, concave goal functionals. We establish the existence and uniqueness of a Nash equilibrium in both the finite-player network game and the corresponding infinite-player graphon game, and prove its convergence as the number of players tends to infinity. We then introduce a central planner who implements a dynamic targeted intervention. Given a fixed budget, the central planner maximizes the average welfare at equilibrium by perturbing the players' heterogeneous goal functionals. Using a novel fixed-point argument, we prove the existence and uniqueness of an optimal intervention in the graphon setting, and show that it achieves near-optimal performance in large finite networks. Finally, we study the special case of linear-quadratic goal functionals and derive semi-explicit solutions for the optimal intervention.
This is a joint work with Sturmius Tuschmann.