Alternating-announcements cheap talk

We model alternating-announcements cheap talk, while discussing the efficiency consequences of explicitly allowing the 'no-agreement' outcome of the game with communication to vary with players' cheap talk announcements. Our results give further consistency to the argument that a cheap talk extension does not necessarily imply efficiency in the play of the original game. Moreover, we characterize the extent of such inefficiency, and show it to be similar to that obtained by Rabin [Rabin, M., 1994. Journal of Economic Theory 63, 370-391], despite the strategic incentives driving our results differing from Rabin's. We also show that efficiency is obtained when the history of alternating announcements is ignored when an agreement is not reached.