Sparse control selects few agents for optimal opinion influence
Sparse One-Step-Ahead Optimal Control of Time-Varying Affine Opinion Networks: Tracking and Competitive Games
Computer Science and Game Theory
Summary
This paper looks at how to influence people's opinions in a changing social network by targeting only a few individuals at a time. The authors study a model where the network's opinions evolve according to known rules, and a controller chooses which individuals to influence and by how much, but with limited resources. They found a way to pick the best few agents to target quickly by sorting certain values, making the control efficient and exact. When multiple influencers compete, the interactions have predictable equilibrium behavior, and the authors show how competition changes the outcomes.
What this means in practice
- •For social media platform operators: Select minimal key users to efficiently shift network opinions in dynamic user groups with resource limits.
- •For political campaign strategists: Identify few influencers to target dynamically for optimal sway on voter opinions under resource constraints.
Authors
Gabriel Gentil, Amit Bhaya
Abstract
This paper studies resource-limited external influence in time-varying opinion networks when a controller must choose both a small set of agents and a scalar intervention at each update. We use the affine free response, which includes DeGroot and Friedkin--Johnsen dynamics, followed by a direct sparse action. Eliminating the scalar action reduces the one-step problem to a cardinality-constrained support objective whose global optimum is obtained from the largest or smallest residual components. Hence exact sparse one-step-ahead optimal control requires one sort and \(O(|\mathcal T|\log|\mathcal T|)\) operations, where \(\mathcal T\) is the support set. For periodic affine dynamics, the resulting state-dependent low-rank feedback admits cycle-based ultimate bounds and exact tracking of model-invariant targets. The DeGroot and Friedkin--Johnsen specializations expose the role of target invariance and the affine mismatch term. With several competing external players, each sparse best response retains the same sorting structure and the complete binary--continuous stage game is an exact potential game, so a pure-strategy equilibrium exists at every frozen state. Same-state welfare benchmarks separate loss due to scalar competition from the additional loss due to strategic support selection. Numerical examples validate exact support selection and illustrate switching-order effects, DeGroot/Friedkin--Johnsen tracking, resource tradeoffs, and competitive implementations.