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

Abstract

In this paper, we deepen the analysis of continuous time Fictitious Play\nlearning algorithm to the consideration of various finite state Mean Field Game\nsettings (finite horizon, $\\gamma$-discounted), allowing in particular for the\nintroduction of an additional common noise.\n We first present a theoretical convergence analysis of the continuous time\nFictitious Play process and prove that the induced exploitability decreases at\na rate $O(\\frac{1}{t})$. Such analysis emphasizes the use of exploitability as\na relevant metric for evaluating the convergence towards a Nash equilibrium in\nthe context of Mean Field Games. These theoretical contributions are supported\nby numerical experiments provided in either model-based or model-free settings.\nWe provide hereby for the first time converging learning dynamics for Mean\nField Games in the presence of common noise.\n