We investigate the problem of generating informative questions in information-asymmetric conversations. Unlike previous work on question generation which largely assumes knowledge of what the answer might be, we are interested in the scenario where the questioner is not given the context from which answers are drawn, but must reason pragmatically about how to acquire new information, given the shared conversation history. We identify two core challenges: (1) formally defining the informativeness of potential questions, and (2) exploring the prohibitively large space of potential questions to find the good candidates. To generate pragmatic questions, we use reinforcement learning to optimize an informativeness metric we propose, combined with a reward function designed to promote more specific questions. We demonstrate that the resulting pragmatic questioner substantially improves the informativeness and specificity of questions generated over a baseline model, as evaluated by our metrics as well as humans.