Agent i Set of Influence I$_{i}$ I$_{i}$ = { , , , , } , j$_{1}$ j$_{2}$ j$_{3}$ i j$_{4}$ S p$_{ij}$ =  1/3 p$_{ii}$ =  1 p$_{is}$ FIG. 1: Social interaction between agent i and its neighbors. Each neighbor is inclu ded with probability p$_{ij}$$_{α}$ into the set of influence I$_{i}$. The agent i is also included with probability p$_{ii}$ = 1. The agent s , included with probability p$_{is}$ according to Eq. (1) represents a super-agent which acts over the whole society. This allows a self-reflection of agent i about its own traits when comparing with the traits of its neighbors. Then, each agent is aware of its own traits when being influenced by its neighbors and its own traits count when deciding to change, or not, its corresponding value for a different one. Figure 1 illustrates the social influence procedure. In the example shown, the agent i selected has cultural traits (1,1,1) and the neighborhood is formed by the one-step neighbors (von Neumann neighborhood). We have also supposed that all the four neighbors have entered into the set of influence I$_{i}$. In general, neighbors are included according to the probabilities p$_{ij}$ , computed for each neighbor. The last agent to be included on the set I$_{i}$ is an agent shared by all the agents on the network. Without loss of generality this super-agent s is set up with culture zero in all of its trait values and never change them. This global agent represents a Mass Media influence which acts over the whole society. Its inclusion in this model follows the same rules explained on Ref. [29], according to which the probability of interaction between this super-agent with an agent i of the society is given by where O$_{is}$ is the overlap between the agent i and the super-agent s . The parameter ϵ ( > 0) p$_{is}$ = O$_{is}$ + ϵ F + ϵ (1) 6