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 about it in the literatute; moreover, these contributions mainly deal with counterfeiting employing a model 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 dynamical system and relevant to its solution and its asymptotic behaviour. Nevertheless, because of the presence of nonlinearities and stochastics, these results are not able to fully characterize the proposed dynamical system; so, in order to fill this deficiency, we also carry out a numerical investigation with a Swarm-based code.