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Mean Field Game of Mutual Holding with common noise
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We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, the problem exhibits the standard paradigm of mean--variance trade off. Our crucial observation is to search for equilibrium solutions of our mean field game among those models which satisfy an appropriate notion of no--arbitrage. Under this condition, it follows that the representative agent optimization step is reduced to a standard portfolio optimization problem with random endowment.
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Fast and slow mean-field games
An averaged, common-noise-free mean-field game equilibrium induces an approximate Nash equilibrium for a two-scale common-noise mean-field game, with error O(delta^(1/6)) or O(delta^(1/3)).
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