  The paper is concerned with the simultaneous solution of a very large number
of optimization problems the structure of which is not given in the outset and
is dynamically agreed upon while a large number of optimizers work in an
orchestra. The proposed new approach to such problems was prompted by the
surprising discovery that the common strategy, adopted in a large body of
research, for producing time-invariant equilibrium in the classical
Aiyagari-Bewley-Huggett model fails to achieve its objective in a widely cited
benchmark study, with the implication that a central problem in macroeconomics
has been without an adequate solution, and despite recent advances based on
novel mathematical techniques borrowed from the theory of mean field games. It
is shown that the intrinsic structure of a generic heterogeneous agent
incomplete market model imposes connections across time that existing
mathematical frameworks cannot capture. The new technique is shown to provide
numerically verifiable equilibria in some widely researched, yet still
unsolved, concrete instances of heterogeneous agent models. The scope of "the
approximate aggregation conjecture" of Krusell and Smith (still an open problem
in macroeconomics) is clarified and a new computational strategy, which does
not rely on simulation or the need to postulate infinite time horizon, for
models with common shocks is developed. New insights about the fluctuations in
the population distribution in such models are drawn and some novel closed-form
expressions are obtained.
