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Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications

[Submitted on 5 Jul 2020 (v1), last revised 26 Oct 2020 (this version, v2)]

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Abstract: In this paper, we deepen the analysis of continuous time Fictitious Play
learning algorithm to the consideration of various finite state Mean Field Game
settings (finite horizon, $gamma$-discounted), allowing in particular for the
introduction of an additional common noise.


We first present a theoretical convergence analysis of the continuous time
Fictitious Play process and prove that the induced exploitability decreases at
a rate $O(frac{1}{t})$. Such analysis emphasizes the use of exploitability as
a relevant metric for evaluating the convergence towards a Nash equilibrium in
the context of Mean Field Games. These theoretical contributions are supported
by numerical experiments provided in either model-based or model-free settings.
We provide hereby for the first time converging learning dynamics for Mean
Field Games in the presence of common noise.

Submission history

From: Sarah Perrin [view email]

[v1]
Sun, 5 Jul 2020 23:31:47 UTC (2,790 KB)

[v2]
Mon, 26 Oct 2020 11:18:44 UTC (1,202 KB)

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