Strategic interpretations

We study strategic communication when the sender's multi-dimensional messages are given an interpretation by the sender himself or by a proxy. Interpreting messages involves the provision of some data about their statistical state-dependence. Interpretation can be selective: different kinds of data interpret different sets of message components. The receiver uses this data to decipher messages, yet he does not draw any inferences from the kind of data he is given. In this way, strategic interpretation of messages can influence the receiver's understanding of their equilibrium meaning. We show that in a two-action, two-state setting, the sender can attain his first-best payoff when the prior on one state exceeds a threshold that decays quickly with message dimensionality. We examine the result's robustness to the critique that our receiver does not attempt any inferences from selective interpretations.