Mathematisches Seminar

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

02.05.2019 von 10:15 bis 11:45

LMS 4 - Raum 325 - Seminarhörsaal

Abstract:

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.

Einladender: S. Christensen

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