Opinions and Networks: How Do They Effect Each Other

The topic of this study is two-fold and two models are presented. For the first part, I propose a non-linear learning algorithm that takes into account both proximity of opinions and network effects. Agents reach consensus of a final opinion that can be estimated given initial conditions under star and small-world networks. However, when the network structure is scale-free, simulation results show rather chaotic patterns. In the second half of this paper, a two-stage endogenous network formation mechanism is introduced. Opinion closeness is critical in establishing links. Existing neighbors also play an important role in connecting to new neighbors, which, combined with a growing population, contributes to a power-law degree distribution with coefficients that fit empirical findings extremely well. The correlation between opinion and degree is illustrated and formalized as well.