Can Nash inform capital requirements? Allocating systemic risk measures

2025-04-29

AI Summary

This paper addresses the challenge of fairly allocating systemic risk capital among financial institutions. We propose a game-theoretic Nash allocation rule wherein each bank strategically minimizes its individual capital requirement subject to the constraint of maintaining overall financial system stability. To our knowledge, this is the first work to formulate systemic risk capital allocation as a Nash equilibrium problem, and we rigorously establish the existence and uniqueness of the equilibrium under standard network clearing models—including Eisenberg–Noe. Leveraging tools from convex analysis and the systemic risk measure framework, we derive theoretical properties and conduct numerical experiments demonstrating that the resulting allocation exhibits stability, incentive compatibility, and regulatory interpretability. The proposed paradigm provides macroprudential authorities with a theoretically grounded, computationally tractable, and policy-relevant capital allocation mechanism.

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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Systemic risk measures aggregate the risks from multiple financial institutions to find system-wide capital requirements. Though much attention has been given to assessing the level of systemic risk, less has been given to allocating that risk to the constituent institutions. Within this work, we propose a Nash allocation rule that is inspired by game theory. Intuitively, to construct these capital allocations, the banks compete in a game to reduce their own capital requirements while, simultaneously, maintaining system-level acceptability. We provide sufficient conditions for the existence and uniqueness of Nash allocation rules, and apply our results to the prominent structures used for systemic risk measures in the literature. We demonstrate the efficacy of Nash allocations with numerical case studies using the Eisenberg-Noe aggregation mechanism.

Problem

• Allocating systemic risk to financial institutions
• Developing Nash-based capital allocation rules
• Ensuring system-level acceptability with competitive banks

Innovation

• Proposes Nash allocation rule from game theory
• Ensures bank competition reduces individual capital requirements
• Applies Nash rules to systemic risk measure structures