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Recent advances in multi-agent reinforcement learning (MARL) have achieved super-human performance in games like Quake 3 and Dota 2. Unfortunately, these techniques require orders-of-magnitude more training rounds than humans and don't generalize to new agent configurations even on the same game. In this work, we propose Collaborative Q-learning (CollaQ) that achieves state-of-the-art performance in the StarCraft multi-agent challenge and supports ad hoc team play. We first formulate multi-agent collaboration as a joint optimization on reward assignment and show that each agent has an approximately optimal policy that decomposes into two parts: one part that only relies on the agent's own state, and the other part that is related to states of nearby agents. Following this novel finding, CollaQ decomposes the Q-function of each agent into a self term and an interactive term, with a Multi-Agent Reward Attribution (MARA) loss that regularizes the training. CollaQ is evaluated on various StarCraft maps and shows that it outperforms existing state-of-the-art techniques (i.e., QMIX, QTRAN, and VDN) by improving the win rate by 40% with the same number of samples. In the more challenging ad hoc team play setting (i.e., reweight/add/remove units without re-training or finetuning), CollaQ outperforms previous SoTA by over 30%.