報告題目：Minimal solutions of master equations for extended mean field games
報 告 人：牟宸辰 教授
所在單位：香港城市大學
報告時間：2024年5月22日 10:00-11:00
報告地點：數學樓第一報告廳
校内聯系人：王春朋 wangcp@jlu.edu.cn
報告摘要：In an extended mean field game, the vector field governing the flow of the population can be different from that of the individual player at some mean field equilibrium. This new class strictly includes the standard mean field games. It is well known that, without any monotonicity conditions, mean field games typically contain multiple mean field equilibria and the wellposedness of their corresponding master equations fails. In this paper, a partial order for the set of probability measure flows is proposed to compare different mean field equilibria. The minimal and maximal mean field equilibria under this partial order are constructed and satisfy the flow property. The corresponding value functions, however, are in general discontinuous. We thus introduce a notion of weak-viscosity solutions for the master equation and verify that the value functions are indeed weak-viscosity solutions. Moreover, a comparison principle for weak-viscosity semi-solutions is established and thus these two value functions serve as the minimal and maximal weak-viscosity solutions in appropriate sense.
In particular, when these two value functions coincide, the value function becomes the unique weak-viscosity solution to the master equation. The novelties of the work persist even when restricted to the standard mean field games. This is based on a joint work with Jianfeng Zhang.
報告人簡介：牟宸辰，香港城市大學助理教授，于2016年獲得美國佐治亞理工學院的數學博士學位，2016-2020年間在加州大學洛杉矶分校做博士後，主要從事平均場博弈理論的研究工作，已在JEMS, Memoirs of the AMS, Ann. Probab., Ann. Appl. Probab., Anal. PDE, Comm. Math. Phys., Trans. Amer. Math. Soc.等國際權威期刊上發表論文數篇。
