Nonlinear banking duopoly model with capital regulation: The case of Italy

We analyse a nonlinear banking duopoly model with capital regulation and asymmetric costs. We follow the literature on banking and capital regulation focusing on Italian banks. We extend the banking duopoly model with nonlinear costs of Brianzoni and Campisi (2021), by introducing the hyperbolic inverse demand function, following Puu (1991). In this way, we include a further nonlinear component in the model consisting of nonlinear demand of loans. We proceed in two parts. First, we concentrate on the analysis of the local stability of the model. Given the high number of parameters, we support the analytical study with several numerical simulations. In the second part, we focus on the conditions under which small banks are more efficient than large banks. For this purpose, we study the dynamics of loans when different parameters vary simultaneously. Our results confirm the empirical evidence that small banks play a central role in supporting local firms and families more than large banks.