Cheap Talk and Sequential Equilibria in Signaling Games

https://doi.org/0012-9682(199607)64:4<917:CTASEI>2.0.CO;2-P
p. 917-942

Alejandro M. Manelli

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.