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

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.