# Leading the Pack: N-player Opponent Shaping

arXiv: https://arxiv.org/abs/2312.12564 · HTML: https://mlsanity.com/paper/2312.12564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [Stable Opponent Shaping in Differentiable Games](https://mlsanity.com/paper/1811.08469/) (2018)
- [DiCE: The Infinitely Differentiable Monte-Carlo Estimator](https://mlsanity.com/paper/1802.05098/) (2018)
- [Model-Free Opponent Shaping](https://mlsanity.com/paper/2205.01447/) (2022)
- [A Policy Gradient Algorithm for Learning to Learn in Multiagent Reinforcement Learning](https://mlsanity.com/paper/2011.00382/) (2020)
- [COLA: Consistent Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/2203.04098/) (2022)
- [Proximal Learning With Opponent-Learning Awareness](https://mlsanity.com/paper/2210.10125/) (2022)
- [Adversarial Cheap Talk](https://mlsanity.com/paper/2211.11030/) (2022)

## Abstract (arXiv)

Reinforcement learning solutions have great success in the 2-player general sum setting. In this setting, the paradigm of Opponent Shaping (OS), in which agents account for the learning of their co-players, has led to agents which are able to avoid collectively bad outcomes, whilst also maximizing their reward. These methods have currently been limited to 2-player game. However, the real world involves interactions with many more agents, with interactions on both local and global scales. In this paper, we extend Opponent Shaping (OS) methods to environments involving multiple co-players and multiple shaping agents. We evaluate on over 4 different environments, varying the number of players from 3 to 5, and demonstrate that model-based OS methods converge to equilibrium with better global welfare than naive learning. However, we find that when playing with a large number of co-players, OS methods' relative performance reduces, suggesting that in the limit OS methods may not perform well. Finally, we explore scenarios where more than one OS method is present, noticing that within games requiring a majority of cooperating agents, OS methods converge to outcomes with poor global welfare.