Trust, influence, and convergence of behavior in social networks

I propose a social learning framework where agents repeatedly take the weighted average of all agents’ current opinions in forming their own for the next period. They also update the influence weights that they place on each other. It is proven that both opinions and the influence weights are convergent. In the steady state, opinions reach consensus and influence weights are distributed evenly. Convergence occurs with an extended model as well, which indicates the tremendous influential power possessed by a minority group. Computer simulations of the updating processes provide supportive evidence.