Communication with endogenous deception costs

We study how the suspicion that communicated information might be deceptive affects the nature of what can be communicated in a sender-receiver game. Sender is said to deceive Receiver if she sends a message that induces a belief that is different from the belief that should have been induced in the realized state. Deception is costly to Sender and the cost is endogenous: it is increasing in the distance between the induced belief and the belief that should have been induced. A message function that induces Sender to engage in deception is not credible and cannot be part of an equilibrium. We study credible communication with state-dependent and state-independent Sender's preferences. The cost of deception parametrizes the sender's ability to commit to her strategy. Through varying this cost, our model spans the range from cheap talk, or no commitment (Crawford and Sobel, 1982) to full commitment (Kamenica and Gentzkow, 2011).