Optimal Multiphase Investment Strategies for Influencing Opinions in a Social Network

TL;DR

This paper develops a model for multi-phase investment strategies in social networks to influence opinions, deriving equilibrium strategies and analyzing the impact of initial biases on investment decisions.

Contribution

It introduces a multi-phase opinion influence model extending DeGroot-Friedkin, deriving Nash equilibria, and providing polynomial algorithms for optimal budget allocation in competitive settings.

Findings

Higher initial bias weights lead to increased first-phase investment.

Nash equilibria exist and can be computed efficiently in two-camp scenarios.

Optimal budget splitting can be determined in polynomial time.

Abstract

We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camp's influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time.