Communication under language barriers

We study the welfare effect of language barriers in communication. Specifically, we compare the equilibrium welfare in a game with language barriers to that in the equivalent game without language barriers. We show how and why language barriers may (weakly) improve welfare by providing two positive results. First, in a game with any language barriers, we prove that if we allow for N-dimensional communication, any equilibrium outcome of the equivalent game without language barriers can be replicated. Second, for any payoff primitive, we provide a welfare ranking for several noisy-communication devices, including language barriers, that generalizes the results in Goltsman et al. (2009). In particular, our results imply that there always exist some language barriers whose maximal equilibrium welfare (always weakly and sometimes strictly) dominates any noisy-talk equilibrium (and hence also any cheap-talk equilibrium) under no language barriers.