Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
