The topology of interactions has been proved very influential in the results of models based on
learning and evolutionary game theory. This paper is aimed at investigating the effect of structures
ranging from regular ring lattices to random networks, including small-world networks, in a
model focused on property distribution norms. The model considers a fixed and finite population
of agents who play the Nash bargaining game repeatedly. Our results show that regular networks
promote the emergence of the equity norm, while less-structured networks make possible the
appearance of fractious regimes. Additionally, our analysis reveals that the speed of adoption can
also be affected by the network structure
