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Exploration under sparse rewards is a key challenge for multi-agent reinforcement learning problems. One possible solution to this issue is to exploit inherent task structures for an acceleration of exploration. In this paper, we present a novel exploration approach, which encodes a special structural prior on the reward function into exploration, for sparse-reward multi-agent tasks. Specifically, a novel entropic exploration objective which encodes the structural prior is proposed to accelerate the discovery of rewards. By maximizing the lower bound of this objective, we then propose an algorithm with moderate computational cost, which can be applied to practical tasks. Under the sparse-reward setting, we show that the proposed algorithm significantly outperforms the state-of-the-art algorithms in the multiple-particle environment, the Google Research Football and StarCraft II micromanagement tasks. To the best of our knowledge, on some hard tasks (such as 27m_vs_30m}) which have relatively larger number of agents and need non-trivial strategies to defeat enemies, our method is the first to learn winning strategies under the sparse-reward setting.