Space-time budget allocation policy design for viral marketing

TL;DR

This paper models opinion dynamics in social networks influenced by external marketing campaigns, and develops optimal space-time budget allocation strategies to steer opinions towards a target, revealing key prioritization principles.

Contribution

It introduces a formal model of hybrid opinion dynamics with external influence and derives optimal budget allocation policies for targeted opinion control.

Findings

Marketers should prioritize certain agents based on influence and initial conditions.

Optimal budget allocation often involves investing early and using water-filling strategies.

Numerical examples validate the proposed allocation policies.

Abstract

We address formally the problem of opinion dynamics when the agents of a social network (e.g., consumers) are not only influenced by their neighbors but also by an external influential entity referred to as a marketer. The influential entity tries to sway the overall opinion as close as possible to a desired opinion by using a specific influence budget. We assume that the exogenous influences of the entity happen during discrete-time advertising campaigns; consequently, the overall closed-loop opinion dynamics becomes a linear-impulsive (hybrid) one. The main technical issue addressed is finding how the marketer should allocate its budget over time (through marketing campaigns) and over space (among the agents) such that the agents' opinion be as close as possible to the desired opinion. Our main results show that the marketer has to prioritize certain agents over others based on their initial condition, their influence power in the social graph and the size of the cluster they belong to. The corresponding space-time allocation problem is formulated and solved for several special cases of practical interest. Valuable insights can be extracted from our analysis. For instance, for most cases, we prove that the marketer has an interest in investing most of its budget at the beginning of the process and that budget should be shared among agents according to the famous water-filling allocation rule. Numerical examples illustrate the analysis.