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In natural language, referencing objects at different levels of specificity is a fundamental pragmatic mechanism for efficient communication in context. We develop a novel communication game, the hierarchical reference game, to study the emergence of such reference systems in artificial agents. We consider a simplified world, in which concepts are abstractions over a set of primitive attributes (e.g., color, style, shape). Depending on how many attributes are combined, concepts are more general ("circle") or more specific ("red dotted circle"). Based on the context, the agents have to communicate at different levels of this hierarchy. Our results show that the agents learn to play the game successfully and can even generalize to novel concepts. To achieve abstraction, they use implicit (omitting irrelevant information) and explicit (indicating that attributes are irrelevant) strategies. In addition, the compositional structure underlying the concept hierarchy is reflected in the emergent protocols, indicating that the need to develop hierarchical reference systems supports the emergence of compositionality.