Abstract concepts are a hallmark of human cognition and culture. However, there is debate over how they are cognitively represented, and how they emerge and become conventionalized within a community. One influential approach is that abstract concepts are based on conceptual metaphors. This study investigates the emergence and conventionalization of abstract concepts and metaphors in an experimental-semiotic referential communication game in which participants communicate abstract concepts and metaphors via drawing. The study sheds light on the different strategies participants use to evoke abstract concepts and shows that participants decrease the number of strategies they use over subsequent rounds of interaction, converging on more successful strategies and thereby initiating a joint process of conventionalization. Acknowledgements: This research is part of the project No. 2021/43/P/HS2/02729 co-funded by the National Science Centre and the European Union Framework Programme for Research and Innovation Horizon 2020 under the Marie Skodowska-Curie grant agreement No. 945339.