Dynamic threshold models of collective action in social networks

We intend to understand how decentralized planning through local interactions can result in large-scale change from inactivity to global action cascades characteristic of social revolutions as well as innovation adoption. Building on the dynamic threshold model of threshold learning and collection action proposed in [1], this paper investigates the diffusion process in a number of canonical graph structures with heterogeneous agents. We solve the dynamic equations for star, ring, and infinite path topologies. Of special interest are the situations in which action becomes ubiquitous. When this is not the case, we formulate the radius of diffusion as the farthest reach of action from a core of instigators situated in a network of like-minded risk-averse agents. It is shown that full connectivity in a social network can sometimes hinder collective action. Based on the structure of the network and initial thresholds, the model leads the network to one of the possible equilibria of the game on the underlying graph or results in oscillation. Thus the model in this paper predicts non-monotone participation and heterogeneous outcomes, providing a more realistic model of mobilization, innovation diffusion, and opinion reversal.