Sequential Equilibria and Cheap Talk in Infinite Signaling Games. Part 2: Cheap Talk - Karl Iorio; Alejandro M. Manelli (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 1993)
Signaling games with infinite action spaces may have no sequential equilibrium. We prove that adding cheap talk to these games solves the non-existence problem; the sequential equilibrium outcome correspondence is upper hemi-continuous. In addition, when the signaling space has sufficiently many signals, any cheap talk sequential equilibrium outcome can be appproximated by a sequential (e)-equilibrium of the game without cheap talk. In these cases, adding cheap talk does not fundamentally alter the nature of the game.
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