Analysis of opinion dynamics under binary exogenous and endogenous signals

Abstract

We propose and analyze a stochastic model for opinion dynamics over social networks. In the scenario considered, each agent has an opinion level which belongs to a discrete set. At any given time, the agent takes an action 0 or 1 depending on the opinion, and this action can be seen as a binary signal that can influence the other agents in the network. The opinion updates based on the signal from a random neighbor or from an external entity who attempts to manipulate or control the network. In the absence of the external signal or a constant signal, this model is shown to asymptotically produce consensus with a finite number of connected agents. Additionally, the consensus is determined by the signal. On the other hand, when the number of agents is large, the time to achieve consensus can become exponentially large and the dynamics exhibit population equilibrium points that are ”metastable”. These equilibria can be observed with a finite (but large) number of agents through numerical simulations and are shown to persist for a long duration.