Paper: arXiv 2504.20413
Authors: Çağın Ararat, Zachary Feinstein
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.
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 3.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides a rigorous mathematical framework using game theory and convex analysis to solve the systemic risk allocation problem, establishing existence and uniqueness conditions. However, it is primarily theoretical with empirical work limited to numerical case studies and simulations rather than extensive empirical backtesting on real historical datasets.
Research Flowchart
flowchart TD
A[Research Goal: Fairly allocate systemic risk capital requirements to individual banks] --> B[Game Theory Methodology: Formulate Nash Allocation Rule via competitive game]
B --> C[Inputs & Models: Systemic risk measures & Eisenberg-Noe interbank network]
C --> D[Mathematical Analysis: Derive conditions for existence & uniqueness of Nash equilibrium]
D --> E[Numerical Case Studies: Simulate network distress and capital allocation]
E --> F[Outcomes: Unique, stable capital allocations that maintain system-level safety]
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1 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.