This paper presents the models and main results of Allen e Gale (2000)Allen, F. & Gale, D. (2000). Financial contagion. Journal of Political Economy, 108(1):1-33. and Bertolai et alii (2016)Bertolai, J. D., Cavalcanti, R. d. O., & Monteiro, P. K. (2016). Bank runs with many small banks and mutual guarantees at the terminal stage. Mimeo. as limiting cases of the society's problem in choosing the optimal banking system. Next, complementary results to these references are established. Alternative approaches to banking fragility are studied, highlighting the effects of imposing the sequential service constraint on the choice of the optimal banking system. The first contribution is complementary to the contagion result of Allen e Gale (2000)Allen, F. & Gale, D. (2000). Financial contagion. Journal of Political Economy, 108(1):1-33. and shows that there exists an intervention in the interbank market that eliminates the widespread collapse of the banking system caused by the contagion. In the second contribution, the bank-run's existence result of Bertolai et alii (2016)Bertolai, J. D., Cavalcanti, R. d. O., & Monteiro, P. K. (2016). Bank runs with many small banks and mutual guarantees at the terminal stage. Mimeo. is generalized. In their results, everyone but the last depositor (or the last two depositors) participate in the bank run. For arbitrary k, we establish under which conditions only the last k depositors in each bank do not participate in the bank run by keeping their resources invested in the banking system.
