Dynamic Network Influence: The Art of Strategic Messaging

Abstract

Strategic influencers send costly messages over time to persuade a network of agents. Each influencer maximizes her total discounted payoff, which decreases as agents' opinions deviate from her agenda. Agents update their opinions by averaging neighbors' opinions and influencers' messages. A planner, acting as a single influencer, sends more extreme early messages to accelerate agenda adoption and moderate messages later to achieve convergence. The planner fares worse in networks where agents assign more uneven weights to their own opinions and those of their neighbors. With multiple influencers, agents reach consensus in symmetric networks, which is a weighted average of the influencers' agendas. The consensus is independent of the network and the agents' initial opinions. In asymmetric networks, influencers with different impacts often target different subgroups of agents endogenously, leading to perpetual disagreement.

Keywords: optimal dynamic intervention in social networks, strategic competition among influencers, consensus and perpetual disagreements