Skewed information transmission: The effect of complementarities in a multi-dimensional cheap talk game

We analyze a cheap talk game in a two-dimensional framework, with complementarities between the dimensions. A receiver chooses a two-dimensional costly effort in a productive activity. The Receiver’s effort profile is determined by his individual ability profile, of which he is unaware. He is advised by an informed Sender, who makes one of two recommendations to maximize the Receiver’s output. Output is a Constant Elasticity of Substitution function of the Receiver’s two one-dimensional contributions. The credibility constraint on the Sender’s recommendations requires her to truthfully contrast the Receiver’s abilities. As a result, the Receiver associates greater (resp. less) effort with greater (resp. less) perceived ability in one (resp. the other) dimension. However, when there are strong complementarities, the Sender becomes more interested in the mismatch between effort and ability. Thus, strong complementarities preclude the Sender from making credible recommendations. By contrast, weaker complementarities allow the Sender to make credible recommendations, using either: (i) a symmetric comparison of abilities; or (ii) an asymmetric comparison, in which one ability could be perceived as greater, even if it is not. Sufficient complementarities make the asymmetric information revelation more stable and more productive.