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arXiv · 1110.3441

From infinity to one: The reduction of some mean field games to a global control problem

Olivier Guéant
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Abstract

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.

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Olivier Guéant. 2011-10-15. From infinity to one: The reduction of some mean field games to a global control problem. https://arxiv.org/abs/1110.3441

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