CHEAP TALK AND SEQUENTIAL EQUILIBRIA IN SIGNALING GAMES

Well-behaved infinite signaling games may have no sequential equilibri a. We prove that adding cheap talk to these games ''solves'' the nonex istence problem: the limit of sequential equilibrium outcomes of finit e approximating games is a sequential equilibrium outcome of the cheap -talk extension of the limit game. In addition, when the signaling spa ce has no isolated points, any cheap-talk sequential equilibrium outco me can be approximated by a sequential epsilon-equilibrium of the game without cheap talk.