The Battling Influencers Game: Nash Equilibria Structure of a Potential Game and Implications to Value Alignment
This addresses the problem of strategic behavior in multi-influencer systems for researchers in game theory and social dynamics, with implications for value alignment, but it is incremental as it builds on existing game-theoretic frameworks.
The paper introduces the Battling Influencers Game (BIG) to model competition among influencers for attention, proving it is a potential game with one or infinite pure Nash equilibria found via convex optimization, and shows that at pure equilibria, all but at most one influencer exaggerate to the maximum extent.
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.