IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00605267.html
   My bibliography  Save this paper

Risk-sharing with self-insurance: the role of cooperation

Author

Listed:
  • Francesca Barigozzi

    () (UNIBO - Università di Bologna [Bologna])

  • Renaud Bourlès

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

  • Dominique Henriet

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

  • Giuseppe Pignataro

    () (Department of Economics - UNIBO - Università di Bologna [Bologna])

Abstract

We analyze mutual insurance arrangements (policies based on risk-sharing among a pool of policyholders) when consumers choose a self-insurance effort, that is an effort decreasing the size of any loss occurring. We consider both cooperative and non-cooperative strategies in the effort choice. Cooperation among policyholders leads to the full internalization of the positive impact the effort exerts on the premium. We show that, for an infinite size of pool, with cooperation first-best efficiency is achieved. Moreover, cooperation is sustained as an equilibrium in a repeated interaction game for a sufficiently low size of pool. An interesting implication of our results is that a cooperative mutual policy can dominate a stock insurance contract. Simulations show that mutual insurance with cooperation as an equilibrium dominates a second-best stock-type insurance policy even when pool size is low.

Suggested Citation

  • Francesca Barigozzi & Renaud Bourlès & Dominique Henriet & Giuseppe Pignataro, 2011. "Risk-sharing with self-insurance: the role of cooperation," Working Papers halshs-00605267, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00605267
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00605267
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-00605267/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mayers, David & Smith, Clifford Jr., 1986. "Ownership structure and control : The mutualization of stock life insurance companies," Journal of Financial Economics, Elsevier, vol. 16(1), pages 73-98, May.
    2. Francesca Barigozzi, 2004. "Reimbursing Preventive Care," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 29(2), pages 165-186, December.
    3. Timothy Besley & Maitreesh Ghatak, 2005. "Competition and Incentives with Motivated Agents," American Economic Review, American Economic Association, vol. 95(3), pages 616-636, June.
    4. Manning, Willard G, et al, 1987. "Health Insurance and the Demand for Medical Care: Evidence from a Randomized Experiment," American Economic Review, American Economic Association, vol. 77(3), pages 251-277, June.
    5. Richard Arnott & Joseph E. Stiglitz, 1988. "Randomization with Asymmetric Information," RAND Journal of Economics, The RAND Corporation, vol. 19(3), pages 344-362, Autumn.
    6. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    7. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    8. James A. Ligon & Paul D. Thistle, 2008. "Moral Hazard and Background Risk in Competitive Insurance Markets," Economica, London School of Economics and Political Science, vol. 75(300), pages 700-709, November.
    9. Igal Hendel & Alessandro Lizzeri, 2003. "The Role of Commitment in Dynamic Contracts: Evidence from Life Insurance," The Quarterly Journal of Economics, Oxford University Press, vol. 118(1), pages 299-328.
    10. Raj Chetty, 2006. "A New Method of Estimating Risk Aversion," American Economic Review, American Economic Association, vol. 96(5), pages 1821-1834, December.
    11. James A. Ligon & Paul D. Thistle, 2005. "The Formation of Mutual Insurers in Markets with Adverse Selection," The Journal of Business, University of Chicago Press, vol. 78(2), pages 529-556, March.
    12. Ingela Alger & Jörgen W. Weibull, 2010. "Kinship, Incentives, and Evolution," American Economic Review, American Economic Association, vol. 100(4), pages 1725-1758, September.
    13. Pierre Picard, 2014. "Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 153-175, September.
    14. Fafchamps, Marcel & Lund, Susan, 2003. "Risk-sharing networks in rural Philippines," Journal of Development Economics, Elsevier, vol. 71(2), pages 261-287, August.
    15. Elinor Ostrom, 2000. "Collective Action and the Evolution of Social Norms," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 137-158, Summer.
    16. Doherty, Neil A & Dionne, Georges, 1993. "Insurance with Undiversifiable Risk: Contract Structure and Organizational Form of Insurance Firms," Journal of Risk and Uncertainty, Springer, vol. 6(2), pages 187-203, April.
    17. Garance Genicot & Debraj Ray, 2003. "Group Formation in Risk-Sharing Arrangements," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 87-113.
    18. Ehrlich, Isaac & Becker, Gary S, 1972. "Market Insurance, Self-Insurance, and Self-Protection," Journal of Political Economy, University of Chicago Press, vol. 80(4), pages 623-648, July-Aug..
    19. Ignacio Moreno & Francisco J. Vázquez & Richard Watt, 2006. "Can Bonus-Malus Allieviate Insurance Fraud?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 123-151.
    20. Renaud Bourlès & Dominique Henriet, 2012. "Risk-sharing Contracts with Asymmetric Information," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 27-56, March.
    21. Yann Bramoullé & Rachel Kranton, 2007. "Risk Sharing Across Communities," American Economic Review, American Economic Association, vol. 97(2), pages 70-74, May.
    22. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    23. Smith, Bruce D & Stutzer, Michael J, 1990. "Adverse Selection, Aggregate Uncertainty, and the Role for Mutual Insurance Contracts," The Journal of Business, University of Chicago Press, vol. 63(4), pages 493-510, October.
    24. Udry, Christopher, 1995. "Risk and Saving in Northern Nigeria," American Economic Review, American Economic Association, vol. 85(5), pages 1287-1300, December.
    25. Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 243-262, December.
    26. Smith, Bruce D & Stutzer, Michael, 1995. "A Theory of Mutual Formation and Moral Hazard with Evidence from the History of the Insurance Industry," Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 545-577.
    27. Mayers, David & Smith, Clifford W, Jr, 1988. "Ownership Structure across Lines of Property-Casualty Insurance," Journal of Law and Economics, University of Chicago Press, vol. 31(2), pages 351-378, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Louis Lévy-Garboua & Claude Montmarquette & Jonathan Vaksmann & Marie Claire Villeval, 2017. "Voluntary Contributions to a Mutual Insurance Pool," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(1), pages 198-218, February.

    More about this item

    Keywords

    Mutual arrangement; self-insurance; positive externality on the insurance premium; cooperation;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00605267. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.