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

2025-02-03

AI Summary

This paper investigates value distortion arising from influencer competition under the attention economy. We propose the Battling Influencers Game (BIG), the first game-theoretic model framing multi-influencer competition for audience attention as a potential game. We rigorously prove the existence of pure-strategy Nash equilibria and establish their efficient computability via convex optimization. We characterize equilibrium structure—showing uniqueness or uncountable multiplicity—and identify the critical property “at most one honest influencer.” Crucially, we demonstrate that in equilibrium, the majority of influencers rationally adopt extreme content distortion strategies, leading to systemic inauthenticity. This work provides the first foundational game-theoretic explanation of how systemic distortion emerges endogenously from strategic interaction among influencers. It further implies that value alignment requires structural intervention—not merely individual-level regulation—to mitigate strategic cancellation effects that inherently undermine authenticity.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Application Domains: Humanities & Computational Social Science

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

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.

Problem

• Influencer Competition
• Attention Economy
• Value Consistency

Innovation

• BIG Model
• Attention Competition
• Mathematical Equilibrium