The Battling Influencers Game: Nash Equilibria Structure of a Potential Game and Implications to Value Alignment

TL;DR

This paper models competing influencers as a potential game, revealing that influencers tend to exaggerate their actions at equilibrium, with implications for understanding strategic influence and value alignment.

Contribution

It introduces the Battling Influencers Game (BIG), a novel game-theoretic model that characterizes strategic influencer competition and analyzes equilibrium properties.

Findings

BIG is a potential game with pure Nash equilibria found via convex optimization.

At equilibrium, most influencers exaggerate their actions to maximum levels.

Pure Nash equilibria can be either unique or infinite in number.

Abstract

When multiple influencers attempt to compete for a receiver's attention, their influencing strategies must account for the presence of one another. We introduce the Battling Influencers Game (BIG), a multi-player simultaneous-move general-sum game, to provide a game-theoretic characterization of this social phenomenon. We prove that BIG is a potential game, that it has either one or an infinite number of pure Nash equilibria (NEs), and these pure NEs can be found by convex optimization. Interestingly, we also prove that at any pure NE, all (except at most one) influencers must exaggerate their actions to the maximum extent. In other words, it is rational for the influencers to be non-truthful and extreme because they anticipate other influencers to cancel out part of their influence. We discuss the implications of BIG to value alignment.