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Mean field games with absorption and common noise with a model of bank run

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  • Burzoni, Matteo
  • Campi, Luciano

Abstract

We consider a mean field game describing the limit of a stochastic differential game of N-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state space. We provide a general result for the existence of weak mean field equilibria which, due to the absorption and the common noise, are given by random flow of sub-probabilities. We first use a fixed point argument to find solutions to the mean field problem in a reduced setting resulting from a discretization procedure and then we prove convergence of such equilibria to the desired solution. We exploit these ideas also to construct ɛ-Nash equilibria for the N-player game. Since the approximation is two-fold, one given by the mean field limit and one given by the discretization, some suitable convergence results are needed. We also introduce and discuss a novel model of bank run that can be studied within this framework.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:164:y:2023:i:c:p:206-241
    DOI: 10.1016/j.spa.2023.07.007
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    References listed on IDEAS

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