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Cheap Talk and Sequential Equilibria in Signaling Games
Alejandro M. Manelli
Abstract
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.
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