Skip to main content
SpringerLink
Log in

Threshold models of mutual insurance

  • Mathematical Game Theory and Applications
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Game-theoretic models of mutual insurance are considered. Here a player chooses between participating in a mutual insurance fund or not. Player’s behavior depends on its risk aversion. Using a scalar coefficient of agent’s risk aversion degree, we define utility functions leading to the threshold behavior of agents. Next, the game-theoretic models of anonymous and non-anonymous insurants are studied and Nash equilibrium conditions are established for both models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Breer, V.V., Game-Theoretic Models of Collective Conformity Behavior, Autom. Remote Control, 2012, vol. 73, no. 10, pp. 1680–1692.

    Article  MATH  MathSciNet  Google Scholar 

  2. Breer, V.V., A Game-Theoretic Model of Non-anonymous Threshold Conformity Behavior, Autom. Remote Control, 2012, vol. 73, no. 7, pp. 1256–1264.

    Article  MathSciNet  Google Scholar 

  3. Burkov, V.N., Zalozhnev, A.Yu., Kulik, O.S., and Novikov, D.A., Mekhanizmy strakhovaniya v sotsial’no-ekonomicheskikh sistemakh (Insurance Mechanisms in Socio-economic Systems), Moscow: Inst. Probl. Upravlen., 2002.

    Google Scholar 

  4. Burkov, V.N. and Novikov, D.A., Kak upravlyat’ proektami (How to Manage Projects), Moscow: Sinteg, 1997.

    Google Scholar 

  5. Goubko, M.V. and Novikov, D.A., Teoriya igr v upravlenii organizatsionnymi sistemami (Game Theory and Organizational Systems Control), Moscow: Sinteg, 2002.

    Google Scholar 

  6. Ivashkin, E.I., Vzaimnoe strakhovanie (Mutual Insurance), Moscow: Ross. Ekonom. Akad., 2000.

    Google Scholar 

  7. von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behavior, New York: Wiley, 1953. Translated under the title Teoriya igr i ekonomicheskoe povedenie, Moscow: Nauka, 1970.

    MATH  Google Scholar 

  8. Novikov, D.A., Insurance Mechanisms: Risk Redistribution and Data Manipulation, Probl. Bezopasn. Chrezvych. Situats., 1997, no. 5, pp. 44–55.

    Google Scholar 

  9. Obshchestva vzaimnogo strakhovaniya (Mutual Insurance Societies), Turbina, K.E., Ed., Moscow: Ankil, 1994.

    Google Scholar 

  10. Serbinovskii, B.Yu. and Gar’kusha, V.N., Strakhovoe delo (Insurance Business), Rostov-on-Don: Feniks, 2000.

    Google Scholar 

  11. Fishbern, P.C., Utility Theory for Decision Making, New York: Wiley, 1970. Translated under the title Teoriya poleznosti dlya prinyatiya reshenii, Moscow: Nauka, 1978.

    Google Scholar 

  12. Actuarial Science. Advances in the Statistics Science. Festschrift in Honor of Professor V.M. Josh’s 70th Birthday, Dordrecht: Reidel, 1987, vol. 6.

  13. Granovetter, M., Threshold Models of Collective Behavior, AJS, 1978, vol. 83, no. 6, pp. 1420–1443.

    Google Scholar 

  14. Pratt, J., Risk Aversion in the Small and in the Large, Econometrica, 1964, vol. 52, no. 1, pp. 122–136.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    V. V. Breer & D. A. Novikov

Authors
  1. V. V. Breer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Novikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Breer.

Additional information

Original Russian Text © V.V. Breer, D.A. Novikov, 2011, published in Matematicheskaya Teoriya Igr i Priloszheniya, 2011, No. 4, pp. 3–22.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Breer, V.V., Novikov, D.A. Threshold models of mutual insurance. Autom Remote Control 76, 897–908 (2015). https://doi.org/10.1134/S0005117915050148

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915050148

Keywords

Search

Navigation