Informed seller problem : signaling, information design, and mechanism design

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This thesis studies an informed seller problem in which the seller tries to signal her private information through different channels—information disclosure, selling mechanism and return policy. Chapter 1 analyzes the signalling effect of information disclosure and price posting. Any separating equilibria must have the two types of seller setting different disclosure rules as well as different prices. Furthermore, the outcome that survives the intuitive criterion always exists and is unique. This equilibrium outcome is separating, for which a closed-form solution is provided. The signaling concern forces the high-type seller to disclose an inefficient amount of information and charge a higher price, resulting in fewer sales and lower profit. A regulation on minimal quality could potentially damage social welfare. In chapter 2, the seller is allowed to design a grand mechanism in which she herself participates in addition to information disclosure. The RSW (Rothschild-Stiglitz-Wilson) mechanism is fully characterized, in which each type of seller separates at the lowest cost. In this mechanism, the low-type seller sells to the buyer with certainty and leaves zero surplus to the buyer. The high-type seller discloses to the buyer whether his value is above a cutoff, sets a payment difference equal to the conditional expected value, and provides a nonnegative bonus. Furthermore, the RSW mechanism can always be supported as a PBE and its outcome is the unique PBE outcome under certain conditions. Finally, the RSW mechanism always survives the Intuitive criterion, and is the unique one under certain conditions. Chapter 3 studies an second-price auction with return policies. It starts with binary type. In the separating equilibria, the high-type seller’s return policy needs to be generous enough to deter the low-type seller from mimicking. Notably, a better return policy may not correspond to a better type. In the pooling equilibria, the return policy cannot be too generous. All separating equilibria have the same outcome and all survive Eso and Schummer’s credible deviation criterion while all pooling equilibria fail. Separation is costless and efficient. Similar results apply when sellers have multiple types.
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