Opinion dynamics of random-walking agents on a lattice

Abstract: Opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or non-periodic. At each time step, all agents move randomly on the lattice, and update their opinions based on those of neighbors with whom the differences of opinions are not greater than a given threshold. Due to the effect of repeated averaging, opinions first converge locally, and eventually reach steady states. Like other models with bounded confidence, steady states in general are those with one or more opinion groups, in which all agents have the same opinion. When both the lattice and the opinion are periodic, however, metastable states, in which the whole spectrum of location-dependent opinions can coexist, can emerge. This result shows that, when a set of continuous opinions forms a structure like a circle, other that a typically-used linear opinions, rich dynamic behavior can arise. When there are geographical restrictions in reality, a complete consensus is rarely reached, and metastable states here can be one of the explanations for these situations, especially when opinions are not linear.