Unraveling of product information with discrete prices

In a market with discrete prices, the seller provides verifiable information to buyers with privately known tastes, possibly horizontally differentiated. We present a necessary and sufficient condition, called the unraveling criteria, to achieve effective unraveling at every prudent rationalizable outcome, which extends pairwise monotonicity in a more general framework. The unraveling criteria are satisfied if we can rank seller types from the ones with the highest to the ones with the lowest sales at every price, reminiscent of vertical differentiation. We observe that cautiousness, embodied in prudent rationalizability, plays a specific role in achieving effective unraveling.