Title: Revisiting the Monotonicity Constraint in Cooperative Multi-Agent Reinforcement Learning. Abstract: QMIX, a popular MARL algorithm based on the monotonicity constraint, has been used as a baseline for the benchmark environments, such as Starcraft Multi-Agent Challenge (SMAC), Predator-Prey (PP). 
Recent variants of QMIX target relaxing the monotonicity constraint of QMIX to improve the expressive power of QMIX, allowing for performance improvement in SMAC. 
However, we find that such performance improvements of the variants are significantly affected by various implementation tricks. In this paper, we revisit the monotonicity constraint of QMIX,
(1) we design a novel model RMC to further investigate the monotonicity constraint; the results show that monotonicity constraint can improve sample efficiency in some purely cooperative tasks;
(2) we then re-evaluate the performance of QMIX and these variants by a grid hyperparameter search for the tricks; the results show QMIX achieves the best performance among them, achieving SOTA performance on SMAC and PP;
(3) we analyze the monotonic mixing network from a theoretical perspective and show that it can represent any tasks which can be interpreted as purely cooperative. These analyses demonstrate that relaxing the monotonicity constraint of the mixing network will not always improve the performance of QMIX, which breaks our previous impressions of the monotonicity constraints.