Special Semester in Probability Lectures

Title: Mean Field Games with finite states in the weak formulation, and application to contract theory

Abstract:Models for Mean Field Games (MFGs) with finite state spaces are typically introduced using controlled Markov chains and studied through the solutions of Hamilton-Jacobi-Belman and Fokker-Planck equations. We introduce the weak formulation based on change of measure techniques for stochastic integral equations and prove existence and uniqueness in this setting. We then apply these results to a contract theory problem in which a principal faces a field of agents interacting in a mean field manner. We reduce the problem to the optimal control of dynamics of the McKean-Vlasov type, and we solve this problem explicitly in a special case reminiscent of the linear - quadratic mean field game models. We conclude with a numerical example of epidemic containment.

https://www.math.uconn.edu/research/seminars/show-poster/?TalkID=15743