Partial credence goods on review platforms

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We study a repeated credence goods market in which experts provide treatment to customers. We assume that the history of transactions is recorded on a review platform that contains information only about treatments, and not about non-treatments. We also introduce the notion of a partial credence good, where treated customers receive a noisy, ex post signal about the necessity of treatment. Absent such signals, there is a breakdown of the market. We provide a necessary and sufficient condition on the signals that guarantees the existence of any non-trivial equilibrium, as well as an efficient one.