Competitive insurance pricing in a duopoly

A single-period stochastic insurance duopoly is formulated to examine the pre-assignment of roles to the insurance game’s players. This paper considers two information structures. In the first structure, one insurer assumes the role of the Stackelberg leader by setting the premium first, while the competitor, acting as the Stackelberg follower, responds after observing the leader’s premium. In the second structure, both insurers act as Nash players, setting premiums simultaneously without considering the competitor’s premium. This paper shows the existence of Stackelberg and Nash equilibria in these settings and identifies which information structure leads to superior utility when the decision to disclose the premium to the competitor is endogenous. A decision game is developed to determine the conditions under which both insurers prefer sequential over simultaneous premium setting in terms of utility.