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

arXiv: https://arxiv.org/abs/2502.01127 · HTML: https://mlsanity.com/paper/2502.01127/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 17 of 17)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Whose Opinions Do Language Models Reflect?](https://mlsanity.com/paper/2303.17548/) (2023)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Fine-tuning language models to find agreement among humans with diverse preferences](https://mlsanity.com/paper/2211.15006/) (2022)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [RLHF from Heterogeneous Feedback via Personalization and Preference Aggregation](https://mlsanity.com/paper/2405.00254/) (2024)
- [PAL: Pluralistic Alignment Framework for Learning from Heterogeneous Preferences](https://mlsanity.com/paper/2406.08469/) (2024)
- [Truthful Aggregation of LLMs with an Application to Online Advertising](https://mlsanity.com/paper/2405.05905/) (2024)
- [Mechanism Design for LLM Fine-tuning with Multiple Reward Models](https://mlsanity.com/paper/2405.16276/) (2024)
- [Online Prediction with Selfish Experts](https://mlsanity.com/paper/1702.03615/) (2017)
- [Simultaneous Preference and Metric Learning from Paired Comparisons](https://mlsanity.com/paper/2009.02302/) (2020)
- [Online Learning from Strategic Human Feedback in LLM Fine-Tuning](https://mlsanity.com/paper/2412.16834/) (2024)
- [Actively Learning Hemimetrics with Applications to Eliciting User Preferences](https://mlsanity.com/paper/1605.07144/) (2016)

## Built on by (most cited first, 1 of 1)

- [AI Alignment through a Game-theoretic Lens: A Survey](https://mlsanity.com/paper/2608.27910/) (2026)

## Abstract (arXiv)

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.