Abstract: Guessing games are a prototypical instance of the ``learning by interacting'' paradigm. This work investigates how well an artificial agent can benefit from playing guessing games when later asked to perform on novel NLP downstream tasks such as Visual Question Answering (VQA). We propose two ways to exploit playing guessing games: 1) a supervised learning scenario in which the agent learns to mimic successful guessing games and 2) a novel way for an agent to play by itself, called Self-play via Iterated Experience Learning (SPIEL). We evaluate the ability of both procedures to generalise: an in-domain evaluation shows an increased accuracy (+7.79) compared with competitors on the evaluation suite CompGuessWhat?!; a transfer evaluation shows improved performance for VQA on the TDIUC dataset in terms of harmonic average accuracy (+5.31) thanks to more fine-grained object representations learned via SPIEL.