Abstract: We
analyze
dynamic
capital
allocation and
risk sharing
between a
principal and
many agents,
who privately
observe their
output. The
state
variables of
the mechanism
design problem
are aggregate
capital and
the
distribution
of
continuation
utilities
across agents.
This gives
rise to a
Bellman
equation in an
infinite
dimensional
space, which
we solve with
mean-field
techniques. We
fully
characterize
the optimal
mechanism and
show that the
level of risk
agents must be
exposed to for
incentive
reasons is
decreasing in
their initial
outside
utility. We
extend
classical
welfare
theorems by
showing that
any
incentive-constrained
optimal
allocation can
be implemented
as an
equilibrium
allocation,
with
appropriate
money issuance
and wealth
taxation by
the principal.
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