An evolutionary model of two competing Species with a memory formalism, applied to the Italian Movies indistries to asses the effects of the Policies for its promotion

Abstract. We study the Italian movies industry from 1966 to 2014 through an evolutionary model of two competing species, Italian and foreign movies, with a memory formalism- (which refers to the experience acquired and the reputation of the firms of a given industry )- by which the first order derivative is substituted by a derivative of fractional order. The evolution of the two species, represented by p and q, in the environment of the Italian cinemas, is conditioned by t, the GDP share devoted to this entertainment in competition with other media. The evolution of p (t) and q (t) may be influenced by endogenous perturbations r(t) brought by changes in the institutions .With the evolutionary model with a derivative of fractional order we show that FUS (Fondo Unico per lo Spettacolo:. Unique Performing Arts Fund), had an initial short positive effect on p(t), merely relenting the decrease of its trend. From 1996 we recorded a recovery to the evolutionary trend of p(t) likely to be imputed to r(t) perturbations by new unconventional methods of financing as regional aid to movies located in their territory to promote local tourism and local products, advertising in the movies. This recovery from 2007, after the introduction of the tax credit, became more pronounced, as the share of new Italian on the new movies in the Italian theatres equalized that of the mid seventy. The market oriented new ways of financing movies gradually made the Italian movies industry a structurally efficient market economy activity with products of cultural quality, competing again in the international market.