We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg setting, which assumes a single monopolistic reinsurer on the supply side, our model accounts for strategic price competition between reinsurers. We argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept for analyzing equilibria in the reinsurance market, and we characterize SPNEs using a set of sufficient conditions. We then examine efficiency properties of the contracts induced by an SPNE, and show that these contracts result in Pareto-efficient allocations. Additionally, we show that under mild conditions, the insurer realizes a strict welfare gain, which addresses the concerns of Boonen and Ghossoub (2022) with the Stackelberg model and thereby ultimately reflects the benefit to the insurer of competition on the supply side. We illustrate this point with a numerical example.

我们研究再保险市场中的均衡，其中多个再保险公司具有异质信念，其中偏好由扭曲风险度量给出，定价通过 Choquet 积分完成。我们以序贯经济博弈的形式构建了一个模型，其中再保险公司比保险公司拥有先发优势，就像斯塔克尔伯格的设置一样。然而，与斯塔克伯格设定不同，斯塔克伯格设定假设供应方有一个垄断再保险公司，我们的模型考虑了再保险公司之间的战略价格竞争。我们认为子博弈完美纳什均衡（SPNE）的概念是分析再保险市场均衡的适当解决方案概念，并且我们使用一组充分条件来描述 SPNE。然后我们检查 SPNE 引发的合约的效率属性，并表明这些合同导致帕累托有效分配。此外，我们表明，在温和的条件下，保险公司实现了严格的福利增益，这解决了以下问题：Boonen 和 Ghossoub (2022)使用 Stackelberg 模型，最终反映了供应方竞争给保险公司带来的好处。我们用一个数值例子来说明这一点。