Benjamin Moll (London School of Economics)

Titre : The Trouble with the Master Equation in Macroeconomics Mean Field Games

Abstract : Macroeconomists and mathematicians cast models with heterogeneous agents as Mean Field Games (MGFs) under the assumption that agents perceive the economy's state and all the relevant transition probabilities for the whole economy ("rational expectations"). These macroeconomics MFGs have a special structure: the Hamilton-Jacobi-Bellman equation for agents' value function depends on the density of agents only through low-dimensional functionals of the density ("equilibrium prices"). When there is common noise, rational expectations imply that decision makers forecast equilibrium prices by forecasting infinite-dimensional densities and solve Bellman equations in which this density is a state variable ("Master equation" a.k.a. "Monster equation"). I argue that the rational expectations assumption -- and, by implication, the Master equation -- is unrealistic, unnecessarily complicates computations, and should be replaced. I outline a stripped down version of the problem in the form of a simple Markov Reward Process which highlights the key mathematical challenge which alternative approaches need to resolve.

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