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.  

Just as parallel threebranes on a smooth manifold are related to string theory on AdS_5 \times S^5, parallel threebranes near a conical singularity are related to string theory on AdS_5 \times X_5 for a suitable X_5. For the example of the conifold singularity Klebanov and Witten conjectured that a string theory on AdS_5 \times X^5 can be described by a certain \mathcal{N}=1 supersymmetric gauge theory. Based primarily on their work (arXiv:hep-th/9807080), I describe the gravitational setup of this correspondence as well as their construction of the field theory, allowing for various checks of the duality.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

TBC