Selling Signals

This paper studies a signaling model in which a strategic player can manipulate the signaling cost. A seller chooses a price schedule for a good, and a buyer with a hidden type chooses how much to purchase as a signal to receivers. When receivers observe the price schedule, the seller charges monopoly prices, and the buyer purchases less than the first-best. In contrast, when receivers do not observe the price schedule, the demand for signals is more elastic. We propose a new refinement, the Quasi-Divinity, to refine the equilibria. In equilibrium, the seller charges lower prices, and the buyer purchases more than when receivers observe the price schedule; the highest buyer types purchase more than the first-best. The model suggests that price transparency benefits the seller but harms the buyer. The model can be applied to schools choosing tuition, retailers selling luxury goods and media companies selling advertisements.