The (non-)robustness of influential cheap talk equilibria when the sender’s preferences are state-independent
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 degree of uncertainty about the sender’s preferences in the spirit of Harsanyi (1973). Introducing small costs of lying as in Kartik (2009), i.e. a small preference for sending the actual state as the message, while removing some influential equilibria, makes others robust to payoff uncertainty. Finally, modelling a small desire to be truthful endogenously, i.e. by taking into account how the receiver interprets the message, may make some influential equilibria robust, but may also remove all influential equilibria.
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