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In the intrinsically motivated skills acquisition problem, the agent is set in an environment without any pre-defined goals and needs to acquire an open-ended repertoire of skills. To do so the agent needs to be autotelic (deriving from the Greek auto (self) and telos (end goal)): it needs to generate goals and learn to achieve them following its own intrinsic motivation rather than external supervision. Autotelic agents have so far been considered in isolation. But many applications of open-ended learning entail groups of agents. Multi-agent environments pose an additional challenge for autotelic agents: to discover and master goals that require cooperation agents must pursue them simultaneously, but they have low chances of doing so if they sample them independently. In this work, we propose a new learning paradigm for modeling such settings, the Decentralized Intrinsically Motivated Skills Acquisition Problem (Dec-IMSAP), and employ it to solve cooperative navigation tasks. First, we show that agents setting their goals independently fail to master the full diversity of goals. Then, we show that a sufficient condition for achieving this is to ensure that a group aligns its goals, i.e., the agents pursue the same cooperative goal. Our empirical analysis shows that alignment enables specialization, an efficient strategy for cooperation. Finally, we introduce the Goal-coordination game, a fully-decentralized emergent communication algorithm, where goal alignment emerges from the maximization of individual rewards in multi-goal cooperative environments and show that it is able to reach equal performance to a centralized training baseline that guarantees aligned goals. To our knowledge, this is the first contribution addressing the problem of intrinsically motivated multi-agent goal exploration in a decentralized training paradigm.