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This paper presents a dynamic game framework to analyze the role of largebanks in the interbank market. By extending existing models, we incorporate amajor bank as a dynamic decision-maker interacting with multiple small banks.Using the mean field game methodology and convex analysis, best-responsetrading strategies are derived, leading to an approximate equilibrium for theinterbank market. We investigate the influence of the large bank on the marketstability by examining individual default probabilities and systemic risk,through the use of Monte Carlo simulations. Our findings reveal that, when thesize of the major bank is not excessively large, it can positively contributeto market stability. However, there is also the potential for negativespillover effects in the event of default, leading to an increase in systemicrisk. The magnitude of this impact is further influenced by the size andtrading rate of the major bank. Overall, this study provides valuable insightsinto the management of systemic risk in the interbank market.

Large Banks and Systemic Risk: Insights from a Mean-Field Game Model