Research seminar “On Stars and Galaxies: Optimal Mechanisms to Utilize Social Influence in Networks” by Vladyslav Nora
A principal wishes to induce an action from a group of agents that belong to a social network. Each agent’s social benefit from taking the action increases with any additional friend/link who takes the action. In addition to the social benefits the principal offers external rewards to agents in order to sustain a unique Nash equilibrium in which all agents take the action.
Our first result solve for the optimal mechanism that minimizes the principal’s expanses. We show that in an optimal mechanism popular agents (with a high numbers of links) receive a preferential treatment by the principal. The second part of the paper characterizes those network architectures that are most favorable for the principal to induce action.
We start with two extreme cases showing that (1) If social benefits only depend on the number of one’s friends who take the action, then the optimal network must be complete (2) if it is determined by the proportion of one’s friends who take the action then a “star” is the optimal architecture. The more interesting cases however are the intermediate ones. In the general/intermediate case we identify a novel architecture which we call “Galaxy.” A Galaxy partitions the set of the network’s nodes into two sets S (called stars) and P (called periphery), with every star node being linked to all nodes, and every periphery node being linked only to stars. We show that, in general, an optimal network must be a galaxy.
We discuss the implication of this finding in terms of the optimal policies of companies such as Facebook and LinkedIn to affect the architecture of the networks they control.