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A generalized Nash equilibrium problem arising in banking regulation: An existence result with Tarski's theorem

Author

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  • Yann Braouezec

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Keyvan Kiani

    (EM - EMLyon Business School, LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - ULCO - Université du Littoral Côte d'Opale - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

Abstract

When hit with an adverse shock, banks that do not comply with capital regulation sell risky assets to satisfy their solvency constraint. When financial markets are imperfectly competitive, this naturally gives rise to a GNEP. We consider a new framework with an arbitrary number of banks and assets, and show that Tarski's theorem can be used to prove the existence of a Nash equilibrium when markets are sufficiently competitive. We also prove the existence of ϵ-Nash equilibria.

Suggested Citation

  • Yann Braouezec & Keyvan Kiani, 2023. "A generalized Nash equilibrium problem arising in banking regulation: An existence result with Tarski's theorem," Post-Print hal-03967896, HAL.
    • Handle: RePEc:hal:journl:hal-03967896
    DOI: 10.1016/j.orl.2022.12.003
    Note: View the original document on HAL open archive server: https://hal.science/hal-03967896v1
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    References listed on IDEAS

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    1. Tathagata Banerjee & Zachary Feinstein, 2019. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," Papers 1910.12130, arXiv.org, revised Feb 2021.
    2. Banerjee, Tathagata & Feinstein, Zachary, 2021. "Price mediated contagion through capital ratio requirements with VWAP liquidation prices," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1147-1160.
    3. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    4. Feinstein, Zachary, 2020. "Capital regulation under price impacts and dynamic financial contagion," European Journal of Operational Research, Elsevier, vol. 281(2), pages 449-463.
    5. Agostino Capponi & Martin Larsson, 2015. "Price Contagion through Balance Sheet Linkages," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 5(2), pages 227-253.
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    Cited by:

    1. Feinstein, Zachary & Hałaj, Grzegorz, 2023. "Interbank asset-liability networks with fire sale management," Journal of Economic Dynamics and Control, Elsevier, vol. 155(C).
    2. Xiaoqing Ou & Guolin Yu & Yue Zheng, 2025. "Convergence Rate of A Unified Prediction-Correction Algorithm for Linearly Constrained Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-48, August.

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