The political replacement effect in a kinetic model of social dynamics with phase transition

The political replacement effect is an interesting socio-political hypothesis introduced by Acemoglu and Robinson and statistically tested. It may determine, under some conditions, the phenomenon of innovation blocking, possibly leading to economic backwardness in a society. In a previous paper, we have introduced a kinetic model with stochastic evolutive game-type interactions, analyzing the relationship between the level of political competition in a society and the degree of economic liberalization. In the present paper we model we model the possibility of having a sort of phase transition occurring in the system when the phenomenon of blocking of the introduction of technological innovation, intended in a broad sense, appears. Crossing a critical point, the rules of interactions change by means of slightly different transition probabilities nevertheless determining very significant differences in the resulting long-term solutions.