We study efficient risk sharing among risk-averse agents in an economy with a large, finite number of states. Following a random shock to an initial agreement, agents may renegotiate. If they require a minimal utility improvement to accept a new deal, we show the probability of finding a mutually acceptable allocation vanishes exponentially as the state space grows. This holds regardless of agents' degree of risk aversion. In a two-agent multiple-priors model, we find that the potential for Pareto-improving trade requires that at least one agent's set of priors has a vanishingly small measure. Our results hinge on the ``shape does not matter'' message of high-dimensional isoperimetric inequalities.

翻译：我们研究在一个具有大量有限状态的经济体中，风险厌恶型代理人之间的有效风险分担。在初始协议遭受随机冲击后，代理人可能重新协商。如果他们要求最低限度的效用改进才接受新协议，我们证明：随着状态空间的扩大，找到双方均可接受的分配方案的概率呈指数级衰减。这一结论与代理人的风险厌恶程度无关。在一个双代理人多先验模型中，我们发现帕累托改进交易的实现要求至少一个代理人的先验集合具有趋近于零的测度。我们的结果依赖于高维等周不等式所揭示的“形状无关紧要”的核心思想。