Bayesian Social Learning from Consumer Reviews

Bar Ifrach*, Costis Maglaras, Marco Scarsini, Anna Zseleva

*Corresponding author for this work

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Motivated by the proliferation of user-generated product-review information and its widespread use, this note studies a market where consumers are heterogeneous in terms of their willingness to pay for a new product. Each consumer observes the binary reviews (like or dislike) of consumers who purchased the product in the past and uses Bayesian updating to infer the product quality. We show that the learning process is successful as long as the price is not prohibitive, and therefore at least some consumers, with sufficiently high idiosyncratic willingness to pay, will purchase the product irrespective of their posterior quality estimate. We examine some structural properties of the dynamics of the posterior beliefs. Finally, we study the seller's pricing problem, and we show that, if the set of possible prices is finite, then a stationary optimal pricing policy exists. If it costs the seller a constant amount for each additional unit sold, then under the optimal policy learning fails with positive probability.

Original languageEnglish
Pages (from-to)1209-1221
Number of pages13
JournalOperations Research
Issue number5
Publication statusPublished - 2019
Externally publishedYes


  • social learning
  • Bayesian update
  • reviews
  • optimal pricing

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