# Securing Equal Share: A Principled Approach for Learning Multiplayer Symmetric Games

arXiv: https://arxiv.org/abs/2406.04201 · HTML: https://mlsanity.com/paper/2406.04201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 6 Jun 2024.

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

- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Strongly Adaptive Online Learning](https://mlsanity.com/paper/1502.07073/) (2015)
- [Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization](https://mlsanity.com/paper/1807.04252/) (2018)
- [Near-Optimal No-Regret Learning in General Games](https://mlsanity.com/paper/2108.06924/) (2021)
- [Towards Playing Full MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/2011.12692/) (2020)
- [DouZero: Mastering DouDizhu with Self-Play Deep Reinforcement Learning](https://mlsanity.com/paper/2106.06135/) (2021)
- [Suphx: Mastering Mahjong with Deep Reinforcement Learning](https://mlsanity.com/paper/2003.13590/) (2020)
- [Hedging in games: Faster convergence of external and swap regrets](https://mlsanity.com/paper/2006.04953/) (2020)
- [Modeling Strong and Human-Like Gameplay with KL-Regularized Search](https://mlsanity.com/paper/2112.07544/) (2021)
- [Mastering the Game of No-Press Diplomacy via Human-Regularized Reinforcement Learning and Planning](https://mlsanity.com/paper/2210.05492/) (2022)
- [Human-Level Performance in No-Press Diplomacy via Equilibrium Search](https://mlsanity.com/paper/2010.02923/) (2020)
- [Near-Optimal Learning of Extensive-Form Games with Imperfect Information](https://mlsanity.com/paper/2202.01752/) (2022)
- [No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium](https://mlsanity.com/paper/2004.00603/) (2020)
- [Efficient Phi-Regret Minimization in Extensive-Form Games via Online Mirror Descent](https://mlsanity.com/paper/2205.15294/) (2022)

## Abstract (arXiv)

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games, equilibria in multiplayer games are neither unique nor non-exploitable, failing to provide meaningful guarantees when competing against opponents who play different equilibria or non-equilibrium strategies. This gives rise to a series of long-lasting fundamental questions in multiplayer games regarding suitable objectives, solution concepts, and principled algorithms. This paper takes an initial step towards addressing these challenges by focusing on the natural objective of equal share -- securing an expected payoff of C/n in an n-player symmetric game with a total payoff of C. We rigorously identify the theoretical conditions under which achieving an equal share is tractable and design a series of efficient algorithms, inspired by no-regret learning, that provably attain approximate equal share across various settings. Furthermore, we provide complementary lower bounds that justify the sharpness of our theoretical results. Our experimental results highlight worst-case scenarios where meta-algorithms from prior state-of-the-art systems for multiplayer games fail to secure an equal share, while our algorithm succeeds, demonstrating the effectiveness of our approach.