Reference group influence on binary choices dynamics

The recent literature has analyzed binary choices dynamics providing interesting results. Most of these contributions consider interactions within a single group. Nevertheless, in some situations the interaction takes place not only within a single group but also between different groups. In this paper, we investigate the choice dynamics when considering two populations where one serves as a reference group. Considering this influence effect enriches the dynamics. Although the structurally stable resulting dynamics are attracting cycles only, with any positive integer period, the reference group makes the dynamics of the influenced population much more complex. We considered both the possibility that the reference group has the same or the opposite attitude toward the distribution over the choices. We show how the dynamics and the bifurcation structure are modified under the influence of the reference group. Our results illustrate how the propensity to switch choices in the reference groups may, indirectly, affect choices in the first group.