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Rapport Année : 2011

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

Olivier Guéant

Résumé

This paper presents recent results from Mean Field Game theory underlying the intro- duction 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 in [11, 12, 13] and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation (see [14]), 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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Dates et versions

hal-00628531 , version 1 (03-10-2011)

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  • HAL Id : hal-00628531 , version 1

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Olivier Guéant. From infinity to one: The reduction of some mean field games to a global control problem. 2011. ⟨hal-00628531⟩
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