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