Potential Games With Aggregation in Non-Cooperative General Insurance Markets

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.

Non-cooperative dynamic games for general insurance markets

“…This paper constructs two models for determining the premium of general policies in competitive, non-cooperative, insurance markets. In the corresponding literature, there is still little research done on how the insurance premium follows from competition, and responds to changes initiated by competitors (Taylor, 1986;Daykin and Hey, 1990;Emms, 2012;Pantelous and Passalidou, 2015;Wu and Pantelous, 2017). Moreover, despite the fact that in many lines of insurance the presence of underlying cycles has been observed empirically, there is a constant endeavour to understand the dynamics of insurance premiums (Cummins and Outreville, 1987;Rantala, 1988;Doherty and Kang, 1988;Daykin et al, 1994;Winter, 1994;Cummins and Danzon, 1997;Lamm-Tennant and Weiss, 1997;Taylor, 2008;Malinovskii, 2010).…”

“…Insurers' premium strategies are obtained by calculating the NE of the game. Recently, Wu and Pantelous (2017) introduced the concept of aggregate games based on a one-period framework which aggregates market competition by initially characterizing any selected paired insurers' payoff. The existence of NE was guaranteed by proving that the constructed game is a potential game (Monderer and Shapley, 1996;Jensen, 2010).…”

Optimal strategies for a non-linear premium-reserve model in a competitive insurance market

“…In the literature so far as this is presented above, a common assumption is made that there exists a single insurer whose pricing strategy does not cause any reaction in the rest of the market's competitors. Lately, this assumption has been revisited, and some game theoretic approaches have been developed instead (see Emms, 2012;Dutang et al, 2013;Wu & Pantelous, 2016) and references therein for further details. However, further details are omitted in the present paper.…”

Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

“…Emms (2012) and Boonen et al (2018) do consider continuous-time differential games in premium controls, but again based on Taylor (1986) type demand functions of own and market average premium. Boonen et al (2018) in addition present a continuous-time extension of a one-period aggregate game of Wu and Pantelous (2017), involving a price elasticity of demand or market power parameter, and the individual insurer's payoff depending on own premium and an aggregate of market premiums. The models are deterministic and open-loop Nash equilibria are determined.…”