An Evolutionary Game to Study Banks–Firms Relationship: Monitoring Intensity and Private Benefit

The paper analyzes a dynamic evolutionary game between banks and firms whose interaction has always been characterized by conflictual relationships. Banks would like that the funding is spent to achieve the objectives of the projects submitted, whereas firms would allocate these loans to obtain private benefits. Following repli- cator dynamics, we show that banks and firms have predator-prey interactions of the Lotka–Volterra type. Misbehaving firms who seek private benefits are “predators”and banks are their “prey”. We analyze the dynamics emerging from the model and we prove that the stability of equilibria depending on the fundamental parameters which describe the banks–firms interaction. In addition, we compare equilibria in terms of Pareto efficiency computing welfare through the average profits with some numerical applications. Finally, we propose a stochastic replicator dynamics approach in order to assume a perturbation in the population growth rate and we suppose as endogenous the monitoring intensity.