Cheap talk with transparent and monotone motives from a seller to an informed buyer

We develop a model of cheap talk with transparent and monotone motives from a seller to an informed buyer. By transparent and monotone motives, we mean that the seller's preference does not depend on the state of the world and is increasing in the choice(s) of the buyer regardless of the state of the world. We first show that if the buyer is completely uninformed, only the babbling equilibrium exists. Then, we obtain our main result that even if the buyer has the slightest information, full revelation can be supported by using the crosschecking strategy of the buyer if and only if the seller has a CARA (constant absolute risk aversion) utility function unless the buyer has too much information. In this equilibrium, the buyer can punish the seller who sends a message far above the buyer's information by ignoring the seller's message. Paradoxically, no information and too much information of the buyer both eliminate the fully revealing equilibrium with the crosschecking strategy. We also obtain a counterintuitive result that the seller prefers a more informed buyer than a less informed buyer.