On the tradeoff between the law of large numbers and oligopoly in insurance

For a fixed number of customers in an insurance market, changing the number of insurance firms creates both scale effects on the individual firms (as the number of customers per firm is altered), and an oligopolistic effect on market supply. The most prominent effect of scale is the impact on solvency associated with the law of large numbers (LLN). In this paper, we focus on the relationship between the LLN and the oligopolistic effect of the number of firms in the market, and use a game-theoretic model of insurance market equilibrium to study this problem. For constant absolute risk averse buyers and risk neutral sellers, we find that there is a natural tradeoff between the effects of the LLN and oligopoly that causes both equilibrium quantity and the equilibrium payoff to customers to possess unique interior maxima over the number of insurance firms.