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Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium

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  • Michiko Ogaku

Abstract

This paper investigates whether an ex-ante welfare-maximising risk allocation rule can be implemented among many participants. Specifically, we investigate the applicability of the price and choose mechanism proposed by Echenique and N\'u\~nez(2025) to risk allocation problems. While their mechanism implements Pareto optimal allocations in finite choice sets, we consider extending it to an infinite choice set of feasible risk-sharing allocations. This paper asks whether an ex-ante welfare-maximising risk allocation rule can indeed be implemented for a large group. Specifically, we study the price and choose (P&C) mechanism of Echenique and N\'u\~nez(2025) in a risk-sharing setting. In P&C, players sequentially set prices for each possible alternative; the last player chooses an alternative, provided that all previous players receive the prices they set. Echenique and N\'u\~nez(2025) show that, for finite choice sets, the mechanism implements any Pareto optimal allocation in the subgame-perfect Nash equilibrium. Our setting differs in one crucial respect: the choice set is infinite. Each alternative is a feasible allocation of total risk, and each player sets a Lipschitz-continuous price function on this infinite set. We show that the P&C mechanism can still be extended to implement the allocation that maximises the sum of players' utilities, even with an infinite choice set.

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  • Michiko Ogaku, 2025. "Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium," Papers 2505.04122, arXiv.org.
    • Handle: RePEc:arx:papers:2505.04122
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    References listed on IDEAS

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    1. Michel Denuit & Jan Dhaene & Christian Y. Robert, 2022. "Risk‐sharing rules and their properties, with applications to peer‐to‐peer insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(3), pages 615-667, September.
    2. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2025. "Comonotonicity and Pareto optimality, with application to collaborative insurance," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 1-16.
    3. repec:dau:papers:123456789/361 is not listed on IDEAS
    4. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    5. Abdikerimova, Samal & Feng, Runhuan, 2022. "Peer-to-peer multi-risk insurance and mutual aid," European Journal of Operational Research, Elsevier, vol. 299(2), pages 735-749.
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