Mean Field Games without Rational Expectations
Benjamin Moll, Lenya Ryzhik

TL;DR
This paper develops a framework for mean field games without assuming rational expectations, especially in low-dimensional coupling scenarios, simplifying the analysis by avoiding complex master equations.
Contribution
It introduces a non-rational expectations formulation for MFGs with low-dimensional coupling, enabling simpler finite-dimensional solutions instead of complex master equations.
Findings
Non-rational expectations can replace rational expectations in MFGs.
In low-dimensional coupling MFGs, the master equation can be avoided.
An adaptive learning model exemplifies non-rational expectations in practice.
Abstract
Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common noise, it becomes necessary to solve the "Master equation", in which the infinite-dimensional density of agents is a state variable. The rational expectations assumption and the implication that agents solve Master equations is unrealistic in many applications. We show how to instead formulate MFGs with non-rational expectations. Departing from rational expectations is particularly relevant in "MFGs with a low-dimensional coupling", i.e. MFGs in which agents' running reward function depends on the density only through low-dimensional functionals of this density. This happens, for example, in most macroeconomics MFGs in which these low-dimensional…
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Taxonomy
TopicsGame Theory and Applications · Game Theory and Voting Systems · Economic theories and models
