Chakraborty and Harbaugh (2010) prove the existence of influential cheap talk equilibria in one sender one receiver games when the state is multidimensional and the preferences of the sender are state-independent. We show that only the babbling equilibrium survives the introduction of any small...

Global games with endogenous information often exhibit multiple equilibria. In this paper we show how one can nevertheless identify useful predictions that are robust across all equilibria and that could not have been delivered in the common-knowledge counterparts of these games. Our analysis is...