  We investigate the effects of a large (but finite) state space on models of
efficient risk sharing. A group of risk-averse agents agree on a risk-sharing
agreement in an economy without aggregate risk. The economy is subject to a
perturbation, or shock, that prompts a renegotiation of the agreement. If
agents insist on an $\ep$-utility improvement to accept a new agreement, then
the probability of a post-shock acceptable agreement vanishes exponentially to
zero as the number of states grows. We use similar arguments to consider a
model where agents have multiple prior preferences, and show that the existence
of an $\ep$-Pareto improving trade requires that some sets of priors have
vanishingly small measure. Our results hinge on the "shape does not matter"
message of high dimensional isoperimetric inequalities.
