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Individual and Collective Welfare in Risk Sharing with Many States

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  • Federico Echenique
  • Farzad Pourbabaee

Abstract

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.

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  • Federico Echenique & Farzad Pourbabaee, 2024. "Individual and Collective Welfare in Risk Sharing with Many States," Papers 2401.07337, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2401.07337
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    References listed on IDEAS

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    5. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    6. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
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