Regulation of Rumor Propagation via (Multi-Leader) Stackelberg Graphon Games

TL;DR

This paper models rumor control in large networks using Stackelberg graphon games, introducing a multi-leader framework and an algorithm to analyze how competing influences affect opinion dynamics.

Contribution

It introduces a novel multi-leader Stackelberg graphon game model with equilibrium characterization and a bi-level algorithm for computing equilibria.

Findings

Existence of equilibria is established for the proposed models.

Competing principals lead to strong opinion divisions in the population.

Numerical experiments demonstrate the impact of incentives on rumor spread and opinion polarization.

Abstract

We study the control of rumor propagation in large networked populations by using Stackelberg graphon games. We first introduce a principal who wants to incentivize the spread of her preferred news and discourage the spread of non-preferred news. We define the Stackelberg graphon game equilibrium (SGGE), characterize the graphon game Nash equilibrium (GGNE) with a forward-backward differential equation system, and establish existence results. We further formulate a multi-leader model with two competing principals, each incentivizing her own preferred news. Finally, we propose a bi-level algorithm for computing (multi-leader) Stackelberg graphon game equilibria and conclude with numerical experiments where we show that existence of competing principals will result in strong opinion divisions in the population.