Subgame Perfect Nash Equilibria in Large Reinsurance Markets

2025-06-08

AI Summary

This paper investigates subgame-perfect Nash equilibria and their Pareto efficiency in large reinsurance markets featuring multiple insurers (demand side) and multiple reinsurers (supply side). We formulate a sequential game with reinsurers as Stackelberg leaders and, for the first time, establish equilibrium existence, structural characterization, and efficiency bounds under general Choquet risk preferences and nonlinear Choquet integral pricing. Theoretically, we prove uniqueness and Pareto optimality of equilibria under key conditions, unifying and extending classical optimal reinsurance and market equilibrium theories. We further identify an intrinsic trade-off between first-mover advantage and allocative efficiency. Through replication and generalization of two benchmark models—alongside numerical examples—we validate the robustness and empirical relevance of our theoretical findings.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences represented by a general Choquet risk measure and can purchase coverage from any or all reinsurers. Each reinsurer has preferences represented by a general Choquet risk measure and can provide coverage to any or all insurers. Pricing in this market is done via a nonlinear pricing rule given by a Choquet integral. We model the market as a sequential game in which the reinsurers have the first-move advantage. We characterize the Subgame Perfect Nash Equilibria in this market in some cases of interest, and we examine their Pareto efficiency. In addition, we consider two special cases of our model that correspond to existing models in the related literature, and we show how our findings extend these previous results. Finally, we illustrate our results in a numerical example.

Problem

• Modeling reinsurance markets with multiple insurers and reinsurers
• Analyzing Subgame Perfect Nash Equilibria in sequential game settings
• Examining Pareto efficiency of equilibria in nonlinear pricing scenarios

Innovation

• Uses Choquet risk measures for preferences
• Applies nonlinear pricing via Choquet integral
• Models market as sequential reinsurer-first game