<p>We study the evolution of conventions in a Stag Hunt game where: (i) agents choose a location to interact locally, (ii) interactions are sometimes global and sometimes local, and (iii) agents can be either fine or coarse reasoners, i.e., agents are able or not, respectively, to distinguish between global and local interactions. We show that the structure of interaction and the mode of reasoning affect the selection of social conventions. Further, we find that the coexistence of coarse and fine reasoning may favor or hinder the adoption of the payoff dominant convention—playing Stag—depending on the structure of interaction. In particular, if interactions are mostly local, then fine reasoning increases the diffusion of Stag. Instead, if interactions are sufficiently global, then fine reasoners are never more collaborative than coarse reasoners and they may even disrupt the emergence of payoff dominant conventions.</p>