# Dual Reinforcement Learning Synergy in Resource Allocation: Emergence of Self-Organized Momentum Strategy

arXiv: https://arxiv.org/abs/2509.11161 · HTML: https://mlsanity.com/paper/2509.11161/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 4 of its 73 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 4 of 4)

- [An Introduction to Deep Reinforcement Learning](https://mlsanity.com/paper/1811.12560/) (2018)
- [Coevolution spreading in complex networks](https://mlsanity.com/paper/1901.02125/) (2019)
- [Decoding trust: A reinforcement learning perspective](https://mlsanity.com/paper/2309.14598/) (2023)
- [Decoding fairness: a reinforcement learning perspective](https://mlsanity.com/paper/2412.16249/) (2024)

## Abstract (arXiv)

In natural ecosystems and human societies, self-organized resource allocation and policy synergy are ubiquitous and significant. This work focuses on the synergy between Dual Reinforcement Learning Policies in the Minority Game (DRLP-MG) to optimize resource allocation. Our study examines a mixed-structured population with two sub-populations: a Q-subpopulation using Q-learning policy and a C-subpopulation adopting the classical policy. We first identify a synergy effect between these subpopulations. A first-order phase transition occurs as the mixing ratio of the subpopulations changes. Further analysis reveals that the Q-subpopulation consists of two internal synergy clusters (IS-clusters) and a single external synergy cluster (ES-cluster). The former contribute to the internal synergy within the Q-subpopulation through synchronization and anti-synchronization, whereas the latter engages in the inter-subpopulation synergy. Within the ES-cluster, the classical momentum strategy in the financial market manifests and assumes a crucial role in the inter-subpopulation synergy. This particular strategy serves to prevent long-term under-utilization of resources. However, it also triggers trend reversals and leads to a decrease in rewards for those who adopt it. Our research reveals that the frozen effect, in either the C- or Q-subpopulation, is a crucial prerequisite for synergy, consistent with previous studies. We also conduct mathematical analyses on subpopulation synergy effects and the synchronization and anti-synchronization forms of IS-clusters in the Q-subpopulation. Overall, our work comprehensively explores the complex resource-allocation dynamics in DRLP-MG, uncovers multiple synergy mechanisms and their conditions, enriching the theoretical understanding of reinforcement-learning-based resource allocation and offering valuable practical insights