Cultures are built on social exchange. Most languages have dedicated grammatical machinery for expressing this. To demonstrate that statistical methods can also be applied to grammatical meaning, we here ask whether the underlying meanings of these grammatical constructions are based on shared common concepts. To explore this, we designed video stimuli of reciprocated actions (e.g., "giving to each other" ) and symmetrical states (e.g., "sitting next to each other" ), and with the help of a team of linguists collected responses from 20 languages around the world. Statistical analyses revealed that many languages do, in fact, share a common conceptual core for reciprocal meanings but that this is not a universally expressed concept. The recurrent pattern of conceptual packaging found across languages is compatible with the view that there is a shared non-linguistic understanding of reciprocation. But, nevertheless, there are considerable differences between languages in the exact extensional patterns, highlighting that even in the domain of grammar semantics is highly language-specific.