Nonlinear stochastic dynamics for supply counterfeiting in monopolistic markets

Counterfeiting is a well known world wide phenomenon afflicting several real economies. Notwithstanding the importance of this topic, there are not many works on this topic in the literature; moreover, they mainly deal with counterfeiting with models developed in a static time frame. In this paper we propose, by means of a system of first order nonlinear and stochastic difference equations, a discrete time dynamical model for a monopolistic market characterized by the presence of a supply counterfeiter. More precisely, we determine some theoretical results peculiar to such a dynamics, and relevant to the solution of the model and to its asymptotic behaviour. Nevertheless, because of the presence of nonlinearities and stochastics, these results cannot fully characterize the proposed dynamical system; so, in order to fill this deficiency, we also carry out a numerical investigation by a Swarm based code.

Counterfeiting is a well known world wide phenomenon afflicting several real economies. Notwithstanding the importance of this topic, there are not many works on it in the literature; moreover, they mainly deal with counterfeiting with models developed in a static time frame. In this paper we propose, by means of a system of first order nonlinear and stochastic difference equations, a discrete-time dynamical model for a monopolistic market characterized by the presence of a supply counterfeiter. More precisely, we determine some theoretical results peculiar to such a dynamics, and relevant to the solution of the model and to its asymptotic behaviour. Nevertheless, because of the presence of nonlinearities and stochasticity, these results cannot fully characterize the proposed dynamical system; so, in order to fill this gap, we also carry out a numerical investigation by a Swarm based code.