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POTENTIAL GAMES WITH AGGREGATION IN NON-COOPERATIVE GENERAL INSURANCE MARKETS

Published online by Cambridge University Press:  17 October 2016

Renchao Wu  and
Athanasios A. Pantelous
Renchao Wu
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK, E-Mail: [email protected]
Athanasios A. Pantelous*
Affiliation:
Department of Mathematical Sciences, and Institute for Risk and Uncertainty, University of Liverpool, Liverpool, UK
*
E-Mail: [email protected]
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Abstract

In the global insurance market, the number of product-specific policies from different companies has increased significantly, and strong market competition has boosted the demand for a competitive premium. Thus, in the present paper, by considering the competition between each pair of insurers, an N-player game is formulated to investigate the optimal pricing strategy by calculating the Nash equilibrium in an insurance market. Under that framework, each insurer is assumed to maximise its utility of wealth over the unit time interval. With the purpose of solving a game of N-players, the best-response potential game with non-linear aggregation is implemented. The existence of a Nash equilibrium is proved by finding a potential function of all insurers' payoff functions. A 12-player insurance game illustrates the theoretical findings under the framework in which the best-response selection premium strategies always provide the global maximum value of the corresponding payoff function.

Keywords

Insurance market competitionnon-life insurancepotential game with aggregationpure Nash equilibrium
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 1 , January 2017 , pp. 269 - 302
Copyright
Copyright © Astin Bulletin 2016 

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References

Aase, K.K. (1993) Equilibrium in a reinsurance syndicate; existence, uniqueness and characterization. ASTIN Bulletin, 23 (2), 185–211.CrossRefGoogle Scholar
Alos-Ferrer, C. and Ania, A.B. (2005) The evolutionary stability of perfectly competitive behavior. Economic Theory, 26 (3), 497–516.CrossRefGoogle Scholar
Boonen, T.J. (2015) Competitive equilibria with distortion risk measures. ASTIN Bulletin, 45 (3), 703–728.CrossRefGoogle Scholar
Boonen, T.J. (2016) Nash equilibria of over-the-counter bargaining for insurance risk redistributions: The role of a regulator. European Journal of Operational Research, 250 (3), 955–965.CrossRefGoogle Scholar
Borch, K. H. (1962) Application of game theory to some problems in automobile insurance. ASTIN Bulletin, 2 (2), 208–221.CrossRefGoogle Scholar
Borch, K.H. (1974) The Mathematical Theory of Insurance: An Annotated Selection of Papers on Insurance Published 1960–1972. Mass.: D.C. Heath and Co Lexington.Google Scholar
Brockett, P. and Xia, X. (1995) Operations research in insurance: a review. Transactions of the Society of Actuaries, XLVII, 7–88.Google Scholar
Bühlmann, H. (1980) An economic premium principle. ASTIN Bulletin, 11 (1), 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984) The general economic premium principle. ASTIN Bulletin, 14 (1), 13–21.CrossRefGoogle Scholar
Clapp, J.M. (1985) Quantity competition in spatial markets with incomplete information. The Quarterly Journal of Economics, 100 (2), 519–528.CrossRefGoogle Scholar
Daykin, C.D., Pentikainen, T. and Pesonen, M. (1994) Practical Risk Theory for Actuaries. Suffolk UK: Chapman & Hall/CRC.Google Scholar
Dubey, P., Haimanko, O. and Zapechelnyuk, A. (2006) Strategic complements and substitutes, and potential games. Games and Economic Behavior, 54 (1), 77–94.CrossRefGoogle Scholar
Dutang, C., Albrecher, H. and Loisel, S. (2013) Competition among non-life insurers under solvency constraints: A game-theoretic approach. European Journal of Operational Research, 231 (3), 702–711.CrossRefGoogle Scholar
Emms, P. (2007a) Dynamic pricing of general insurance in a competitive market. ASTIN Bulletin, 37 (01), 1–34.CrossRefGoogle Scholar
Emms, P. (2007b) Pricing general insurance with constraints. Insurance: Mathematics and Economics, 40 (2), 335–355.Google Scholar
Emms, P. (2011) Pricing general insurance in a reactive and competitive market. Journal of Computational and Applied Mathematics, 236 (6), 1314–1332.CrossRefGoogle Scholar
Emms, P. (2012) Equilibrium pricing of general insurance policies. North American Actuarial Journal, 16 (3), 323–349.CrossRefGoogle Scholar
Emms, P. and Haberman, S. (2005) Pricing general insurance using optimal control theory. ASTIN Bulletin, 35 (02), 427–453.CrossRefGoogle Scholar
Emms, P. and Haberman, S. (2009) Optimal management of an insurers exposure in a competitive general insurance market. North American Actuarial Journal, 13 (1), 77–105.CrossRefGoogle Scholar
Emms, P., Haberman, S. and Savoulli, I. (2007) Optimal strategies for pricing general insurance. Insurance: Mathematics and Economics, 40 (1), 15–34.Google Scholar
Fudenberg, D. and Tirole, T. (1991) Game Theory. Cambridge, USA: Massachusetts Institute of Technology Press.Google Scholar
Jensen, M.K. (2010) Aggregative games and best-reply potentials. Economic Theory, 43 (1), 45–66.CrossRefGoogle Scholar
Kukushkin, N.S. (2004) Best response dynamics in finite games with additive aggregation. Games and Economic Behavior, 48 (1), 94–110.CrossRefGoogle Scholar
Lemaire, J. (1984) An application of game theory: Cost allocation. ASTIN Bulletin, 14 (1), 61–81.CrossRefGoogle Scholar
Lemaire, J. (1991) Cooperative game theory and its insurance applications. ASTIN Bulletin, 21 (1), 17–40.CrossRefGoogle Scholar
Lerner, A.P. (1934) The concept of monopoly and the measurement of monopoly power. The Review of Economic Studies, 1 (3), 157–175.CrossRefGoogle Scholar
Malinovskii, V.K. (2010) Competition-originated cycles and insurance strategies. ASTIN Bulletin, 40 (2), 797–843.Google Scholar
Martimort, D. and Stole, L. (2012) Representing equilibrium aggregates in aggregate games with applications to common agency. Games and Economic Behavior, 76 (2), 753–772.CrossRefGoogle Scholar
Monderer, D. and Shapley, L.S. (1996a) Fictitious play property for games with identical interests. Journal of Economic Theory, 68 (1), 258–265.CrossRefGoogle Scholar
Monderer, D. and Shapley, L.S. (1996b) Potential games. Games and Economic Behavior, 14 (1), 124–143.CrossRefGoogle Scholar
Pantelous, A.A. and Passalidou, E. (2013) Optimal premium pricing policy in a competitive insurance market environment. Annals of Actuarial Science, 7 (2), 175–191.CrossRefGoogle Scholar
Pantelous, A.A. and Passalidou, E. (2015) Optimal premium pricing strategies for competitive general insurance markets. Applied Mathematics and Computation, 259, 858–874.CrossRefGoogle Scholar
Pantelous, A.A. and Passalidou, E. (2016) Optimal strategies for a nonlinear premium-reserve model in a competitive insurance market. Annals of Actuarial Science, forthcoming.CrossRefGoogle Scholar
Polborn, M.K. (1998) A model of an oligopoly in an insurance market. The Geneva Papers on Risk and Insurance Theory, 23 (1), 41–48.CrossRefGoogle Scholar
Powers, M.R. and Shubik, M. (1998) On the tradeoff between the law of large numbers and oligopoly in insurance. Insurance: Mathematics and Economics, 23 (2), 141–156.Google Scholar
Powers, M.R., Shubik, M. and Yao, S.T. (1998) Insurance market games: Scale effects and public policy. Journal of Economics, 67 (2), 109–134.CrossRefGoogle Scholar
Rantala, J. (1988) Fluctuations in insurance business results: Some control theoretic aspects. In 23rd International Congress of Actuaries, Vol. R, pp. 43–79.Google Scholar
Rees, R., Gravelle, H. and Wambach, A. (1999) Regulation of insurance markets. The Geneva Papers on Risk and Insurance Theory, 24 (1), 55–68.CrossRefGoogle Scholar
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (2009) Stochastic Processes for Insurance and Finance, volume 505. New York, USA: John Wiley & Sons.Google Scholar
Rothschild, M. and Stiglitz, J. (1976) Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. The Quarterly Journal of Economics, 90 (4), 629–649.CrossRefGoogle Scholar
Rothschild, M. and Stiglitz, J. (1992) Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information. Foundations of Insurance Economics, (eds. Dionne, G. and Harrington, S. E.), pp. 355–375. Huebner International Series on Risk, Insurance and Economic Security, Netherlands: Springer.Google Scholar
Selten, R. (1970) Preispolitik der Mehrproduktenunternehmung in der statischen Theorie, volume 16. Berlin-Heidelberg, Germany: Springer-Verlag.CrossRefGoogle Scholar
Taylor, G.C. (1986) Underwriting strategy in a competitive insurance environment. Insurance: Mathematics and Economics, 5 (1), 59–77.Google Scholar
Taylor, G.C. (1987) Expenses and underwriting strategy in competition. Insurance: Mathematics and Economics, 6 (4), 275–287.Google Scholar
Taylor, G.C. (2008) A simple model of insurance market dynamics. North American Actuarial Journal, 12 (3), 242–262.CrossRefGoogle Scholar
Teugels, J. and Sundt, B. (2004) Encyclopedia of Actuarial Science. New Jersey, USA: John Wiley & Sons.CrossRefGoogle Scholar
Topkis, D.M. (1998) Supermodularity and Complementarity. New Jersey, USA: Princeton University Press.Google Scholar
Tsanakas, A. and Christofides, N. (2006) Risk exchange with distorted probabilities. ASTIN Bulletin, 36 (1), 219–243.CrossRefGoogle Scholar
Voorneveld, M. (2000) Best-response potential games. Economics Letters, 66 (3), 289–295.CrossRefGoogle Scholar