Consensus and Dissensus in Multi-population Multi-agent Systems
May 18, 2023 11:00 AM — 12:00 PM (Montreal time)
This hybrid seminar will take place at HEC Montréal, Hélène-Desmarais room (1st floor, blue sector) and will be webcast via the Zoom platform.
The talk will start with a general overview of mean field games (MFGs) approach to decision making in multi-agent dynamical systems in both model-based and model-free settings and discuss connections to finite-population games. Following this general introduction, the talk will focus on the structured setting of discrete-time infinite-horizon linear-quadratic-Gaussian dynamic games, where the players are partitioned into finitely-many populations with an underlying graph topology—a framework motivated by paradigms where consensus and dissensus co-exist. MFGs approach will be employed to arrive at approximate Nash equilibria, and learning algorithms will be presented for the model-free setting, along with sample complexity analysis.
We consider a dynamic optimization problem where a firm plans their advertising strategy under the uncertainty that their production costs may abruptly increase at any time during the programming interval. We present two approaches that yield a close form solution to this two-stage optimal control problem: a backward approach, where the two periods are solved in reverse order, and a heterogeneous one, where a dedicated version of the maximum principle covers both stages simultaneously. The analytical solution is provided in a simple case, and numerical results are presented for the general case. To evaluate the importance of information about the risk of switching, we compare these results with those of a different scenario, where the planner is unaware of the possible switching time.