Adversarial Social Influence: Modeling Persuasion in Contested Social Networks

TL;DR

This work studies adversarial persuasion in social networks with an arbitrary number of external actors ($P$), introducing the Social Influence Game (SIG) that embeds external budgets into DeGroot-style updates. The problem is shown to be non-convex, formulating a Difference-of-Convex (DC) program, and a scalable Iterated Linear (IL) solver is proposed to approximate solutions via sequential linear programs with Nesterov updates. Empirical results demonstrate that IL achieves solutions within about $7\%$ of a nonlinear solver while being more than $10\times$ faster and scalable to networks with hundreds to thousands of nodes, identifying structural leverage points such as hubs and bridges. The work also designs unbiased reference objectives via a regular simplex of unit-norm targets and provides insight into how influence budgets interact with network topology, offering a foundation for future asymptotic analysis of contested influence in complex networks.

Abstract

We present the Social Influence Game (SIG), a framework for modeling adversarial persuasion in social networks with an arbitrary number of competing players. Our goal is to provide a tractable and interpretable model of contested influence that scales to large systems while capturing the structural leverage points of networks. Each player allocates influence from a fixed budget to steer opinions that evolve under DeGroot dynamics, and we prove that the resulting optimization problem is a difference-of-convex program. To enable scalability, we develop an Iterated Linear (IL) solver that approximates player objectives with linear programs. In experiments on random and archetypical networks, IL achieves solutions within 7% of nonlinear solvers while being over 10x faster, scaling to large social networks. This paper lays a foundation for asymptotic analysis of contested influence in complex networks.

Figures (6)

• Figure 1: The Social Influence Game, where players $A$, $B$, and $C$ are competing to influence the opinions held in the social network made up of the black dots, which represent individuals in the social network. The colored lines represent allocations of influence from the players to individuals in the network.
• Figure 2: The figure shows network topologies generated to evaluate the performance of the solver. The existence of an edge is modeled as a Bernoulli random variable, and the edge weights are randomized in order to obtain a new network.
• Figure 3: The relationship between eigenvector centrality (percentile) and the budget allocations produced by the iterated linear approach follow a hinged pattern, with allocations remaining flat until the eigenvector centrality is in the top decile.
• Figure 4: This plot shows the time taken to solve our optimization problem as the number of individuals in the social networks increases. Only the Iterated Linear solver was able to produce a solution when $M\geq900$ within the computation budget of $2000$ seconds.
• Figure 5: The left side of the figure shows the network and players, along with the influence they allocate. Player three is optimized with the Iterated Linear solver and other players are random. The outlined and annotated circles are the players, and the solid color nodes are the individuals. The right side of the figure shows the reference opinions of each of the players in their colors, and the opinions of each individual in gray.

Theorems & Definitions (3)

• theorem 1: Objective Equivalence
• theorem 2
• Lemma 1