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

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Title: Mean field games with absorption and common noise with a model of bank run.
Authors: Burzoni, Matteo1 (AUTHOR), Campi, Luciano1 (AUTHOR) luciano.campi@unimi.it
Source: Stochastic Processes & Their Applications. Oct2023, Vol. 164, p206-241. 36p.
Subjects: Bank runs, Differential games, Absorption, Games, Nash equilibrium
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. [ABSTRACT FROM AUTHOR]
Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 170721192
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Mean field games with absorption and common noise with a model of bank run.
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  Data: <searchLink fieldCode="AR" term="%22Burzoni%2C+Matteo%22">Burzoni, Matteo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Campi%2C+Luciano%22">Campi, Luciano</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> luciano.campi@unimi.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Stochastic+Processes+%26+Their+Applications%22">Stochastic Processes & Their Applications</searchLink>. Oct2023, Vol. 164, p206-241. 36p.
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  Data: <searchLink fieldCode="DE" term="%22Bank+runs%22">Bank runs</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+games%22">Differential games</searchLink><br /><searchLink fieldCode="DE" term="%22Absorption%22">Absorption</searchLink><br /><searchLink fieldCode="DE" term="%22Games%22">Games</searchLink><br /><searchLink fieldCode="DE" term="%22Nash+equilibrium%22">Nash equilibrium</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.spa.2023.07.007
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 36
        StartPage: 206
    Subjects:
      – SubjectFull: Bank runs
        Type: general
      – SubjectFull: Differential games
        Type: general
      – SubjectFull: Absorption
        Type: general
      – SubjectFull: Games
        Type: general
      – SubjectFull: Nash equilibrium
        Type: general
    Titles:
      – TitleFull: Mean field games with absorption and common noise with a model of bank run.
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            NameFull: Burzoni, Matteo
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            NameFull: Campi, Luciano
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          Dates:
            – D: 01
              M: 10
              Text: Oct2023
              Type: published
              Y: 2023
          Identifiers:
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              Value: 03044149
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            – Type: volume
              Value: 164
          Titles:
            – TitleFull: Stochastic Processes & Their Applications
              Type: main
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