Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T05:55:29.085Z Has data issue: false hasContentIssue false

Cooperative Game Theory and its Insurance Applications

Published online by Cambridge University Press:  29 August 2014

Jean Lemaire*
Affiliation:
Wharton School, University of Pennsylvania, USA
*
Department of Insurance and Risk Management, Wharton School, 3641 Locust Walk, University of Pennsylvania, Philadelphia, PA 19104-6218.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This survey paper presents the basic concepts of cooperative game theory, at an elementary level. Five examples, including three insurance applications, are progressively developed throughout the paper. The characteristic function, the core, the stable sets, the Shapley value, the Nash and Kalai-Smorodinsky solutions are defined and computed for the different examples.

Type
Invited Paper
Copyright
Copyright © International Actuarial Association 1991

References

REFERENCES

Aumann, R. and Maschler, M. (1964) The Bargaining Set for Cooperative Games. Advances in Game Theory, 443–476. Annals of Math. Studies 52, Princeton University Press.Google Scholar
Baton, B. and Lemaire, J. (1981a) The Core of a Reinsurance Market. ASTIN Bulletin 12, 5771.CrossRefGoogle Scholar
Baton, B. and Lemaire, J. (1981b) The Bargaining Set of a Reinsurance Market. ASTIN Bulletin 12, 101114.CrossRefGoogle Scholar
Borch, K. (1960a) Reciprocal Reinsurance Treaties. ASTIN Bulletin 1, 171191.CrossRefGoogle Scholar
Borch, K. (1960b) Reciprocal Reinsurance Treaties Seen as a Two-person Cooperative Game. Skandinavisk Aktuarietidskrift 43, 2958.Google Scholar
Borch, K. (1962) Application of Game Theory to Some Problems in Automobile Insurance. ASTIN Bulletin 2, 208221.CrossRefGoogle Scholar
Borch, K. (1963) Recent Developments in Economic Theory and Their Application to Insurance. ASTIN Bulletin 2, 322341.CrossRefGoogle Scholar
Brams, S., Schotter, A. and Schwodiauer, G., Eds. (1979) Applied Game Theory. IHS-studies 1, Physica-Verlag, 1979.Google Scholar
Briegleb, D. and Lemaire, J. (1982) Calcul des primes et marchandage. ASTIN Bulletin 13, 115131.CrossRefGoogle Scholar
Davis, M. and Maschler, M. (1965) The Kernel of a Cooperative Game. Naval Research Logistics Quarterly 12, 223259.CrossRefGoogle Scholar
Kalai, E. and Smorodinsky, M. (1975) Other Solutions to the Nash Bargaining Problem. Econometrica 43, 513518.CrossRefGoogle Scholar
Lemaire, J. (1974) A New Concept of Value for Games Without Transferable Utilities. International J. of Game Theory 1, 205213.Google Scholar
Lemaire, J. (1977) Echange de risques entre assureurs et théorie des jeux. ASTIN Bulletin 9, 155180.CrossRefGoogle Scholar
Lemaire, J. (1979) A Non Symmetrical Value For Games Without Transferable Utilities. Application to Reinsurance. ASTIN Bulletin 10, 195214.CrossRefGoogle Scholar
Lemaire, J. (1983) An Application of Game Theory: Cost Allocation. ASTIN Bulletin 14, 6181.CrossRefGoogle Scholar
Lucas, W. (1981) Game Theory and Its Applications. Proceedings of Symposia in Applied Maths, American Math. Society Vol 24, Providence, Rhode Island.Google Scholar
Luce, R. and Raiffa, H. (1957) Games and Decisions. John Wiley, New York.Google Scholar
Nash, J. (1950) The Bargaining Problem. Econometrica 18, 155162.CrossRefGoogle Scholar
Owen, G. (1968, 1982) Game Theory. W. Saunders, Philadelphia (first edition). Academic Press, New York (second edition).Google Scholar
Roth, A. (1980) Axiomatic Models of Bargaining. Springer Verlag, Berlin.Google Scholar
Shapley, L. (1953) A Value for n-person Games. Contributions to the Theory of Games Vol II, 307–317. Annals of Mathematics Studies 28, Princeton University Press.Google Scholar
Shapley, L. (1964) Utility Comparisons and the Theory of Games. La décision, CNRS, 251263.Google Scholar
Schmeidler, D. (1969) The Nucleolus of a Characteristic Function Game. SIAM J. Applied Maths., 11631170.Google Scholar
Von Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behaviour. Princeton University Press.Google Scholar