Emergentism and pragmatics are two research fields that study the dynamics of linguistic communication along quite different timescales and intelligence levels. From the perspective of multi-agent reinforcement learning, they correspond to stochastic games with reinforcement training and stage games with opponent awareness, respectively. Given that their combination has been explored in linguistics, in this work, we combine computational models of short-term mutual reasoning-based pragmatics with long-term language emergentism. We explore this for agent communication in two settings, referential games and Starcraft II, assessing the relative merits of different kinds of mutual reasoning pragmatics models both empirically and theoretically. Our results shed light on their importance for making inroads towards getting more natural, accurate, robust, fine-grained, and succinct utterances.