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Participating insurance contracts and the Rothschild-Stiglitz equilibrium puzzle

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  • Pierre Picard

    (Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

We show that an equilibrium always exists in the Rothschild-Stiglitz insurance market model with adverse selection when insurers can offer either non- participating or participating policies, i.e. insurance contracts which may involve policy dividends or supplementary calls for premium. The equilibrium coincides with the Miyazaki- Spence-Wilson equilibrium, which may involves cross-subsidization between contracts within subgroups of individuals. The paper establishes that participating policies act as an implicit threat that dissuades deviant insurers who aim at attracting low risk individuals only. The model predicts that the mutual corporate form should be prevalent in insurance markets or submarkets where second-best Pareto efficiency requires cross-subsidization between risk types. Stock insurers and mutuals may coexist, with stock insurers offering insurance coverage at actuarial price and mutuals cross-subsidizing risks.

Suggested Citation

  • Pierre Picard, 2009. "Participating insurance contracts and the Rothschild-Stiglitz equilibrium puzzle," Working Papers hal-00413825, HAL.
  • Handle: RePEc:hal:wpaper:hal-00413825
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00413825
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    References listed on IDEAS

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    1. Doherty, N.A. & Dionne, G., 1987. "Insurance with Undiversifiable Risk," Cahiers de recherche 8710, Universite de Montreal, Departement de sciences economiques.
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    5. Riley, John G, 1979. "Informational Equilibrium," Econometrica, Econometric Society, vol. 47(2), pages 331-359, March.
    6. 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.
    7. Hellwig, Martin, 1987. "Some recent developments in the theory of competition in markets with adverse selection ," European Economic Review, Elsevier, vol. 31(1-2), pages 319-325.
    8. Engers, Maxim & Fernandez, Luis F, 1987. "Market Equilibrium with Hidden Knowledge and Self-selection," Econometrica, Econometric Society, vol. 55(2), pages 425-439, March.
    9. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
    10. Spence, Michael, 1978. "Product differentiation and performance in insurance markets," Journal of Public Economics, Elsevier, vol. 10(3), pages 427-447, December.
    11. 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.
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    Cited by:

    1. von Siemens, Ferdinand A. & Kosfeld, Michael, 2014. "Team production in competitive labor markets with adverse selection," European Economic Review, Elsevier, vol. 68(C), pages 181-198.
    2. Francesca Barigozzi & Renaud Bourlès & Dominique Henriet & Giuseppe Pignataro, 2017. "Pool size and the sustainability of optimal risk-sharing agreements," Theory and Decision, Springer, vol. 82(2), pages 273-303, February.
    3. Theodoros M. Diasakos & Kostas Koufopoulos, 2011. "Efficient Nash Equilibrium under Adverse Selection," Carlo Alberto Notebooks 215, Collegio Carlo Alberto.
    4. Wanda Mimra & Achim Wambach, 2011. "A Game-Theoretic Foundation for the Wilson Equilibrium in Competitive Insurance Markets with Adverse Selection," CESifo Working Paper Series 3412, CESifo Group Munich.
    5. Anastasios Dosis, 2016. "Investment, Adverse Selection and Optimal Redistributive Taxation," Working Papers hal-01285163, HAL.
    6. Pierre Picard, 2016. "Equilibrium in insurance markets with adverse selection when insurers pay policy dividends," Working Papers hal-01206073, HAL.
    7. 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.
    8. Georges Dionne & Casey Rothschild, 2014. "Economic Effects of Risk Classification Bans," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 184-221, September.
    9. Anastasios Dosis, 2016. "On Signalling and Screening in Markets with Asymmetric Information," Working Papers hal-01285190, HAL.
    10. 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.
    11. Bannier, Christina E. & Feess, Eberhard & Packham, Natalie, 2014. "Incentive schemes, private information and the double-edged role of competition for agents," CFS Working Paper Series 475, Center for Financial Studies (CFS).
    12. Christophe Dutang & Hansjoerg Albrecher & Stéphane Loisel, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," Post-Print hal-01616156, HAL.
    13. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    14. Laurence Ales, 2009. "Adverse Selection and Non-exclusive Contracts," 2009 Meeting Papers 854, Society for Economic Dynamics.
    15. Wanda Mimra & Achim Wambach, 2014. "New Developments in the Theory of Adverse Selection in Competitive Insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 136-152, September.
    16. Anastasios Dosis, 2016. "An Efficient Mechanism for Competitive Markets with Adverse Selection," Working Papers hal-01282772, HAL.
    17. Dosis, Anastasios, 2016. "Investment, Adverse Selection and Optimal Redistributive Taxation," ESSEC Working Papers WP1605, ESSEC Research Center, ESSEC Business School.
    18. Nick Netzer & Florian Scheuer, 2014. "A Game Theoretic Foundation Of Competitive Equilibria With Adverse Selection," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 399-422, May.
    19. Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.
    20. Dosis, Anastasios, 2016. "On Signalling and Screening," ESSEC Working Papers WP1608, ESSEC Research Center, ESSEC Business School.
    21. repec:eee:mateco:v:75:y:2018:i:c:p:140-149 is not listed on IDEAS
    22. Arthur Snow, 2015. "Monopolistic Insurance and the Value of Information," Risks, MDPI, Open Access Journal, vol. 3(3), pages 1-13, July.
    23. Alexander Muermann & Casey Rothschild, 2014. "Guest Editorial—Special Issue “New Developments in the Economics of Insurance Markets with Adverse Selection” of the Geneva Risk and Insurance Review," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 131-135, September.
    24. Georges Dionne & Nathalie Fombaron & Neil Doherty, 2012. "Adverse Selection in Insurance Contracting," Cahiers de recherche 1231, CIRPEE.

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