Abstract-The process by which new ideas, innovations, and behaviors spread through a large social network can be thought of as a networked interaction game: Each agent obtains information from certain number of agents in his friendship neighborhood, and adapts his idea or behavior to increase his benefit. In this paper, we are interested in how opinions, about a certain topic, form in social networks. We model opinions as continuous scalars ranging from 0 to 1 with 1(0) representing extremely positive(negative) opinion. Each agent has an initial opinion and incurs some cost depending on the opinions of his neighbors, his initial opinion, and his stubbornness about his initial opinion. Agents iteratively update their opinions based on their own initial opinions and observing the opinions of their neighbors. The iterative update of an agent can be viewed as a myopic costminimization response (i.e., the so-called best response) to the others' actions. We study whether an equilibrium can emerge as a result of such local interactions and how such equilibrium possibly depends on the network structure, initial opinions of the agents, and the location of stubborn agents and the extent of their stubbornness. We also study the convergence speed to such equilibrium and characterize the convergence time as a function of aforementioned factors. We also discuss the implications of such results in a few well-known graphs including small-world graphs.
Ghaderi and Srikant REF consider a setting where a node iteratively updates its opinion as a myopic best response to the opinions of its own and its neighbors, and hence study how the equilibrium and convergence to it depend on the network structure, initial opinions of the nodes, the location of stubborn agents (forceful nodes with unchanging opinions) and the extent of their stubbornness.
Opinion dynamics in social networks: A local interaction game with stubborn agents
2013 American Control Conference
2013 American Control Conference
Mathematics Computer Science