Cheap talk and sequential equilibria in signaling games

Well-behaved infinite signaling games may have no sequential equilibria. We prove that adding cheap talk to these games ''solves'' the nonexistence problem: the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap-talk extension of the limit game. In addition, when the signaling space has no isolated points, any cheap-talk sequential equilibrium outcome can be approximated by a sequential epsilon-equilibrium of the game without cheap talk.