The (non-)robustness of influential cheap talk equilibria when the sender’s preferences are state independent

Chakraborty and Harbaugh (Am Econ Rev 100(5):2361–2382, 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 influential equilibria do not survive the introduction of any small degree of Harsanyi-uncertainty, i.e., uncertainty about the sender’s preferences in the spirit of Harsanyi (Int J Game Theory 2(1):1–23, 1973).