# Reinforcement Learning In Two Player Zero Sum Simultaneous Action Games

arXiv: https://arxiv.org/abs/2110.04835 · HTML: https://mlsanity.com/paper/2110.04835/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 10 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [Google Research Football: A Novel Reinforcement Learning Environment](https://mlsanity.com/paper/1907.11180/) (2019)
- [Learning with Opponent-Learning Awareness](https://mlsanity.com/paper/1709.04326/) (2017)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [A Survey and Critique of Multiagent Deep Reinforcement Learning](https://mlsanity.com/paper/1810.05587/) (2018)
- [Emergent Complexity via Multi-Agent Competition](https://mlsanity.com/paper/1710.03748/) (2017)
- [Continuous Adaptation via Meta-Learning in Nonstationary and Competitive Environments](https://mlsanity.com/paper/1710.03641/) (2017)
- [Meta-Q-Learning](https://mlsanity.com/paper/1910.00125/) (2019)
- [Managing engineering systems with large state and action spaces through deep reinforcement learning](https://mlsanity.com/paper/1811.02052/) (2018)

## Built on by (most cited first, 4 of 4)

- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Reinforcement Learning Environment with LLM-Controlled Adversary in D&D 5th Edition Combat](https://mlsanity.com/paper/2503.15726/) (2025)
- [Zero-Sum Positional Differential Games as a Framework for Robust Reinforcement Learning: Deep Q-Learning Approach](https://mlsanity.com/paper/2405.02044/) (2024)
- [Adversarial Reinforcement Learning for Offensive and Defensive Agents in a Simulated Zero-Sum Network Environment](https://mlsanity.com/paper/2510.05157/) (2025)

## Abstract (arXiv)

Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum simultaneous action games and discuss the unique challenges this type of game poses. Then we introduce two novel agents that attempt to handle these challenges by using joint action Deep Q-Networks (DQN). The first agent, called the Best Response AgenT (BRAT), builds an explicit model of its opponent's policy using imitation learning, and then uses this model to find the best response to exploit the opponent's strategy. The second agent, Meta-Nash DQN, builds an implicit model of its opponent's policy in order to produce a context variable that is used as part of the Q-value calculation. An explicit minimax over Q-values is used to find actions close to Nash equilibrium. We find empirically that both agents converge to Nash equilibrium in a self-play setting for simple matrix games, while also performing well in games with larger state and action spaces. These novel algorithms are evaluated against vanilla RL algorithms as well as recent state of the art multi-agent and two agent algorithms. This work combines ideas from traditional reinforcement learning, game theory, and meta learning.