Alexander Aurell: Optimal incentives to mitigate epidemics: A Stackelberg mean field game approach

Abstract

Motivated by the models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents.

The individual agent evolves on a finite state space, a setup directly inspired by the compartmental models in epidemiology, and the agents play a non-cooperative game. In this game between the agents, a mean field game, an agent's objective is to minimize her individual cost by controlling her transition rates. The equilibrium the population of agents settles in is controlled by the principal through incentives so as to optimize the principal's objective. The Stackelberg game is analyzed with, by now, standard techniques from the probabilistic approach and special attention is given to a special case: a SIR-type model in which the agents control their contact (or socialization) rate and the principal is a regulator acting with non-pharmaceutical interventions. To compute solutions, a numerical approach based on Monte Carlo simulations and machine learning tools for stochastic optimization is used. Numerical experiments illustrate the impact of the agents’ and the regulator’s Stackelberg equilibrium decisions in two models: the SIR-type model mentioned above, for which we can derive semi-explicit solutions, and in a more complex model which incorporates more states. The talk is based on join work with René Carmona, Gökce Dayanikli, and Mathieu Laurière.

Zoom notes: The passcode for this meeting is 321777. This meeting ID — 621 4469 8204  — will be the recurring meeting for the Statistics and Probability Seminar.