  Referential games and reconstruction games are the most common game types for
studying emergent languages. We investigate how the type of the language game
affects the emergent language in terms of: i) language compositionality and ii)
transfer of an emergent language to a task different from its origin, which we
refer to as language expressivity. With empirical experiments on a handcrafted
symbolic dataset, we show that languages emerged from different games have
different compositionality and further different expressivity.
