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Framework for structural risk analysis of antagonistic systems

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  • Lee, Daeho

Abstract

We propose STAR (Structural Transition Analysis Radar), a mathematical framework for analyzing critical transitions in N-player antagonistic systems. The core function of the framework is to provide an early-warning signal for systemic collapse by calculating risk acceleration, which is defined as the second derivative of a system-wide risk function. This enables the quantitative identification of False Stability—a state in which risk appears stable or declining while structural vulnerability accumulates. The model is grounded in a rigorous game-theoretic foundation: we prove the existence of a Nash equilibrium and, under concavity conditions, establish its local uniqueness. In addition, we introduce a method for static and dynamic sensitivity analysis to evaluate the impact of parameter changes and to optimize intervention strategies. The framework is demonstrated through a conceptual case study of a systemic crisis, presented in Appendix B.

Suggested Citation

  • Lee, Daeho, 2026. "Framework for structural risk analysis of antagonistic systems," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015723
    DOI: 10.1016/j.chaos.2025.117559
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    References listed on IDEAS

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    4. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
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