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We study abstraction in an emergent communication paradigm. In emergent communication, two artificial neural network agents develop a language while solving a communicative task. In this study, the agents play a concept-level reference game. This means that the speaker agent has to describe a concept to a listener agent, who has to pick the correct target objects that satisfy the concept. Concepts consist of multiple objects and can be either more specific, i.e. the target objects share many attributes, or more generic, i.e. the target objects share fewer attributes. We tested two directions of zero-shot generalization to novel levels of abstraction: When generalizing from more generic to very specific concepts, agents utilized a compositional strategy. When generalizing from more specific to very generic concepts, agents utilized a more flexible linguistic strategy that involves reusing many messages from training. Our results provide evidence that neural network agents can learn robust concepts based on which they can generalize using adaptive linguistic strategies. We discuss how this research provides new hypotheses on abstraction and informs linguistic theories on efficient communication.