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Mean field games of timing and models for bank runs

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  • Rene Carmona
  • Francois Delarue
  • Daniel Lacker

Abstract

The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic contributions at the root of our effort, and we develop a mathematical theory for continuous-time stochastic games where the strategic decisions of the players are merely choices of times at which they leave the game, and the interaction between the strategic players is of a mean field nature.

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  • Rene Carmona & Francois Delarue & Daniel Lacker, 2016. "Mean field games of timing and models for bank runs," Papers 1606.03709, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1606.03709
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    References listed on IDEAS

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    Cited by:

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    2. Soren Christensen & Berenice Anne Neumann & Tobias Sohr, 2020. "Competition versus Cooperation: A class of solvable mean field impulse control problems," Papers 2010.06452, arXiv.org, revised Apr 2021.
    3. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    4. Clémence Alasseur & Imen Ben Taher & Anis Matoussi, 2020. "An Extended Mean Field Game for Storage in Smart Grids," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 644-670, February.
    5. Marcel Nutz & Yuchong Zhang, 2021. "Mean Field Contest with Singularity," Papers 2103.04219, arXiv.org.
    6. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    7. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.
    8. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.
    9. Andreea Minca & Johannes Wissel, 2020. "Dynamic Leveraging–Deleveraging Games," Operations Research, INFORMS, vol. 68(1), pages 93-114, January.
    10. Aditya Maheshwari & Andrey Sarantsev, 2017. "Modeling Financial System with Interbank Flows, Borrowing, and Investing," Papers 1707.03542, arXiv.org, revised Oct 2018.
    11. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.
    12. Marcel Nutz & Jaime San Martin & Xiaowei Tan, 2018. "Convergence to the Mean Field Game Limit: A Case Study," Papers 1806.00817, arXiv.org, revised May 2019.
    13. Burzoni, Matteo & Campi, Luciano, 2023. "Mean field games with absorption and common noise with a model of bank run," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 206-241.
    14. Bouveret, Géraldine & Dumitrescu, Roxana & Tankov, Peter, 2022. "Technological change in water use: A mean-field game approach to optimal investment timing," Operations Research Perspectives, Elsevier, vol. 9(C).
    15. Christoph Belak & Daniel Hoffmann & Frank T. Seifried, 2020. "Continuous-Time Mean Field Games with Finite StateSpace and Common Noise," Working Paper Series 2020-05, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    16. Ren'e Carmona & Mathieu Lauri`ere, 2021. "Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance," Papers 2107.04568, arXiv.org.

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