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Pool size and the sustainability of optimal risk-sharing agreements

Author

Listed:
  • Francesca Barigozzi

    (UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna)

  • Renaud Bourlès

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Dominique Henriet

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Giuseppe Pignataro

    (Department of Economics - UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna)

Abstract
We study a risk-sharing agreement where members exert a loss-mitigating action which decreases the amount of reimbursements to be paid in the pool. The action is costly and members tend to free-ride on it. An optimal risk-sharing agreement maximizes the expected utility of a representative member with respect to both the coverage and the (collective) action such that efficiency is restored. We study the sustainability of the optimal agreement as equilibrium in a repeated game with indefinite number of repetitions. When the optimal agreement is not enforceable, the equilibrium with free-riding emerges. We identify an interesting trade-off: welfare generated by the optimal risk-sharing agreement increases with the size of the pool, but at the same time the pool size must not be too large for collective choices to be self-enforcing. This generates a discontinuous effect of pool size on welfare.

Suggested Citation

  • Francesca Barigozzi & Renaud Bourlès & Dominique Henriet & Giuseppe Pignataro, 2017. "Pool size and the sustainability of optimal risk-sharing agreements," Post-Print hal-01505776, HAL.
    • Handle: RePEc:hal:journl:hal-01505776
    DOI: 10.1007/s11238-016-9573-9
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    References listed on IDEAS

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    Cited by:

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    2. Helmuth Cremer & Jean-Marie Lozachmeur, 2024. "Nonlinear Reimbursement Rules for Preventive and Curative Medical Care," CESifo Working Paper Series 11186, CESifo.
    3. Schmeiser, Hato & Orozco-Garcia, Carolina, 2021. "The merits of pooling claims: Mutual vs. stock insurers," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 92-104.

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    More about this item

    Keywords

    Collectively optimal; Loss-mitigating actions; Optimal risk-sharing agreement; Repeated interactions;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • I11 - Health, Education, and Welfare - - Health - - - Analysis of Health Care Markets
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

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