Abstract: In this talk, I’m going to present two recents projects on Stackelberg Mean Field Game. First, we propose and study a class of discrete-time finite-time-horizon mean-field Stack- elberg games, with one leader and an infinite number of identical and indistinguishable followers. The leader may not have control over the response from the followers after she takes an action, and her objective is to maximize her reward considering the worst case cost over all possible ε-Nash equilibria among followers. A new analytical paradigm is established by showing the equivalence between this Stackelberg mean-field game and a minimax optimization problem. This optimization framework facilitates studying both analytically and numerically the set of Nash equilibria; and leads to the the existence, the sensitivity and the robustness analysis of the game value.
Second, we investigate the existence of an optimal policy to monitor a mean field system of agents managing a risky project under moral hazard with accidents modeled by L ́evy processes magnified by the law of the project. We provide a general method to find both a mean field equilibrium for the agents and the optimal compensation policy under general, sufficient and necessary assumptions on all the parameters. We formalize the problem as a bilevel optimization with the probabilistic version of a mean field game which can be reduced to a controlled McKean-Vlasov SDE with jumps. We apply our results to an optimal energy demand-response problem with a crowd of consumers subjected to power cut/shortage when the variability of the energy consumption is too high under endogenous or exogenous strains. In this example, we get an explicit solution to the mean field game and to the McKean-Vlasov equation with jumps.
Bio: I am a postdoctoral researcher in Industrial Engineering & Operations Research Department at Univeristy of California, Berkeley advised by Professor Xin Guo. I obtained my Ph. D. in the Department of Operations Research and Financial Engineering at Princeton University supervised by Professor Daniel Lacker and Professor Mykhaylo Shkolnikov. My research focus lies in the probability and stochastic optimization. I have worked on Mckean-Vlasov type equation, partial differential equations, mathematical financed stochastic control in the past few years.