IDEAS home Printed from https://ideas.repec.org/a/the/publsh/2166.html
   My bibliography  Save this article

Characterization and uniqueness of equilibrium in competitive insurance

Author

Listed:
  • Farinha Luz, Vitor

    (Vancouver School of Economics, University of British Columbia)

Abstract

This paper provides a complete characterization of equilibria in a game-theoretic version of Rothschild and Stiglitz (1976)’s model of competitive insurance. I allow for stochastic contract offers by insurance firms and show that a unique symmetric equilibrium always exists. Exact conditions under which the equilibrium involves mixed strategies are provided. The mixed equilibrium features: (i) cross-subsidization across risk levels, (ii) dependence of offers on the risk distribution and (iii) price dispersion generated by firm randomization over offers.

Suggested Citation

  • Farinha Luz, Vitor, 2017. "Characterization and uniqueness of equilibrium in competitive insurance," Theoretical Economics, Econometric Society, vol. 12(3), September.
    • Handle: RePEc:the:publsh:2166
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20171349/18855/572
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
    2. Veronica Guerrieri & Robert Shimer & Randall Wright, 2010. "Adverse Selection in Competitive Search Equilibrium," Econometrica, Econometric Society, vol. 78(6), pages 1823-1862, November.
    3. Pradeep Dubey & John Geanakoplos, 2002. "Competitive Pooling: Rothschild-Stiglitz Reconsidered," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1529-1570.
    4. 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.
    5. Riley, John G, 1979. "Informational Equilibrium," Econometrica, Econometric Society, vol. 47(2), pages 331-359, March.
    6. 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.
    7. Robert W. Rosenthal & Andrew Weiss, 1984. "Mixed-Strategy Equilibrium in a Market with Asymmetric Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(2), pages 333-342.
    8. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2005. "Default and Punishment in General Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 1-37, January.
    9. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    10. John G. Riley, 2001. "Silver Signals: Twenty-Five Years of Screening and Signaling," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 432-478, June.
    11. Maskin, Eric & Tirole, Jean, 1992. "The Principal-Agent Relationship with an Informed Principal, II: Common Values," Econometrica, Econometric Society, vol. 60(1), pages 1-42, January.
    12. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
    13. V. V. Chari & Ali Shourideh & Ariel Zetlin-Jones, 2014. "Reputation and Persistence of Adverse Selection in Secondary Loan Markets," American Economic Review, American Economic Association, vol. 104(12), pages 4027-4070, December.
    14. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    15. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
    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. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2021. "Competitive Nonlinear Pricing under Adverse Selection," TSE Working Papers 21-1201, Toulouse School of Economics (TSE), revised Aug 2022.
    2. Vitor Farinha Luz, 2022. "Optimal dynamic insurance contracts," Papers 2208.14560, arXiv.org.
    3. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2018. "On competing mechanisms under exclusive competition," Games and Economic Behavior, Elsevier, vol. 111(C), pages 1-15.
    4. Jorge Lemus & Emil Temnyalov & John L. Turner, 2021. "Liability Insurance: Equilibrium Contracts under Monopoly and Competition," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 83-115, February.
    5. Wanda Mimra & Achim Wambach, 2019. "Contract withdrawals and equilibrium in competitive markets with adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 875-907, June.
    6. Levy, Yehuda John & Veiga, Andre, 2020. "On the existence of positive equilibrium profits in competitive screening markets," Games and Economic Behavior, Elsevier, vol. 124(C), pages 140-168.
    7. Dionne, Georges & Fombaron, Nathalie & Mimra, Wanda, 2023. "Adverse selection in insurance," Working Papers 23-5, HEC Montreal, Canada Research Chair in Risk Management.
    8. Kosenko, Andrew & Stiglitz, Joseph & Yun, Jungyoll, 2023. "Bilateral information disclosure in adverse selection markets with nonexclusive competition," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 144-168.
    9. Gemmo, Irina & Kubitza, Christian & Rothschild, Casey, 2020. "Constrained efficient equilibria in selection markets with continuous types," Journal of Public Economics, Elsevier, vol. 190(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wanda Mimra & Achim Wambach, 2019. "Contract withdrawals and equilibrium in competitive markets with adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 875-907, June.
    2. 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.
    3. 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.
    4. Diasakos, Theodoros M. & Koufopoulos, Kostas, 2018. "(Neutrally) Optimal Mechanism under Adverse Selection: The canonical insurance problem," Games and Economic Behavior, Elsevier, vol. 111(C), pages 159-186.
    5. 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.
    6. Dosis, Anastasios, 2018. "On signalling and screening in markets with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 140-149.
    7. Dosis, Anastasios, 2017. "Nash equilibrium in competitive insurance," Economics Letters, Elsevier, vol. 152(C), pages 5-8.
    8. Davoodalhosseini, Seyed Mohammadreza, 2019. "Constrained efficiency with adverse selection and directed search," Journal of Economic Theory, Elsevier, vol. 183(C), pages 568-593.
    9. Pierre Picard, 2019. "Equilibrium in Insurance Markets With Adverse Selection When Insurers Pay Policy Dividends," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(4), pages 887-914, December.
    10. Attar, Andrea & Campioni, Eloisa & Piaser, Gwenaël, 2018. "On competing mechanisms under exclusive competition," Games and Economic Behavior, Elsevier, vol. 111(C), pages 1-15.
    11. Li, Anqi & Xing, Yiqing, 2020. "Intermediated implementation," European Economic Review, Elsevier, vol. 123(C).
    12. Kosenko, Andrew & Stiglitz, Joseph & Yun, Jungyoll, 2023. "Bilateral information disclosure in adverse selection markets with nonexclusive competition," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 144-168.
    13. 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).
    14. 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(2), pages 399-422, May.
    15. De Feo, Giuseppe & Hindriks, Jean, 2014. "Harmful competition in insurance markets," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 213-226.
    16. Ana B. Ania & Thomas Tröger & Achim Wambach, 1998. "An Evolutionary Analysis of Insurance Markets," Vienna Economics Papers vie9808, University of Vienna, Department of Economics.
    17. Zink, Helmut, 1995. "The role of market intransparency in insurance market models," European Journal of Political Economy, Elsevier, vol. 11(2), pages 335-359, June.
    18. Dionne, G. & Doherty, N., 1991. "Adverse Selection in Insurance Markets: a Selective Survey," Cahiers de recherche 9105, Universite de Montreal, Departement de sciences economiques.
    19. Christina E. Bannier & Eberhard Feess & Natalie Packham & Markus Walzl, 2021. "Differentiation and Risk Aversion in Imperfectly Competitive Labor Markets," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 177(1), pages 1-27.
    20. Alessandro Citanna & Paolo Siconolfi, 2016. "Incentive Efficient Price Systems In Large Insurance Economies With Adverse Selection," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 1027-1056, August.

    More about this item

    Keywords

    Asymmetric and private information; mechanism design; oligopoly; economics of contracts; insurance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:the:publsh:2166. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.