Department of Mathematics

Berenice Neumann, Universität Hamburg: "A Myopic Adjustment Process for Mean Field Games with Finite State and Action Space"

May 02, 2019 from 10:15 AM to 11:45 AM

LMS 4 - Raum 325 - Seminarhörsaal


Mean field games formalize dynamic games with a continuum of players and explicit interaction, where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of great interest for socio-economic applications. Since the techniques used for mean field games crucially rely on the assumption that for each population distribution the individual agent has a unique optimal response we introduced a model with finite state and action space not relying on this assumption. In a first part, we propose a toolbox to compute stationary mean field equilibria for these games. In a second part, we introduce, motivated by the fact that it seems unreasonable that agents in these rather complex games coordinate on an equilibrium, a myopic adjustment process. We prove that under certain conditions the process convergences locally and globally towards stationary mean field equilibria, which increases the explanatory power of stationary mean field equilibria.


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