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.

翻译：本文研究了大规模（但有限）状态空间对有效风险分担模型的影响。在一个不存在总体风险的经济体中，一群风险规避的代理人就风险分担协议达成一致。该经济体受到一个扰动或冲击，促使协议重新协商。若代理人坚持要求新协议带来$\ep$的效用改进才予以接受，则随着状态数量增加，冲击后存在可接受协议的概率将以指数速度趋近于零。我们运用类似论证考察了代理人具有多先验偏好的模型，并证明$\ep$-帕累托改进交易的存在要求某些先验集合的测度趋近于零。我们的结论依赖于高维等周不等式所揭示的“几何形态无关紧要”的核心思想。