# Deviations from the Nash equilibrium in a two-player optimal execution game with reinforcement learning

arXiv: https://arxiv.org/abs/2408.11773 · HTML: https://mlsanity.com/paper/2408.11773/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 8 of 8)

- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Double Deep Q-Learning for Optimal Execution](https://mlsanity.com/paper/1812.06600/) (2018)
- [Reinforcement Learning for Quantitative Trading](https://mlsanity.com/paper/2109.13851/) (2021)
- [Multi-Agent Deep Reinforcement Learning for Liquidation Strategy Analysis](https://mlsanity.com/paper/1906.11046/) (2019)
- [Trading algorithms with learning in latent alpha models](https://mlsanity.com/paper/1806.04472/) (2018)
- [A state-constrained differential game arising in optimal portfolio liquidation](https://mlsanity.com/paper/1312.7360/) (2013)
- [Interbank lending with benchmark rates: Pareto optima for a class of singular control games](https://mlsanity.com/paper/2005.05766/) (2020)

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

- [Beyond Supra-Competitive Outcomes: Collusive Behaviour in Deep Reinforcement Learning for Optimal Execution Games](https://mlsanity.com/paper/2610.00619/) (2026)

## Abstract (arXiv)

The use of reinforcement learning algorithms in financial trading is becoming increasingly prevalent. However, the autonomous nature of these algorithms can lead to unexpected outcomes that deviate from traditional game-theoretical predictions and may even destabilize markets. In this study, we examine a scenario in which two autonomous agents, modelled with Double Deep Q-Learning, learn to liquidate the same asset optimally in the presence of market impact, under the Almgren-Chriss (2000) framework. We show that the strategies learned by the agents deviate significantly from the Nash equilibrium of the corresponding market impact game. Notably, the learned strategies exhibit supra-competitive solution, {which might be compatible with a tacit collusive behaviour}, closely aligning with the Pareto-optimal solution. We further explore how different levels of market volatility influence the agents' performance and the equilibria they discover, including scenarios where volatility differs between the training and testing phases.