What is the optimal mechanism that a monopolist should use to sell multiple goods to a single buyer? Despite being a classic economic problem, multi-dimensional screening is notoriously intractable. Even if the seller has just two goods and the buyer's values are additive, independent and identically distributed, the optimal mechanism is hard to characterize generally. The goal of this project is to study a general version of this problem (with arbitrarily many goods) but with the added feature that we include the buyer's learning about his valuation prior to interacting with the seller into the analysis. In a symmetric setting we identify the buyer-optimal outcome, that is, the buyer-optimal learning (which we model as observing a signal about his values) and the corresponding best-response of the seller (the optimal mechanism). We show that, under the buyer-optimal signal, the seller maximizes profits by pure bundling. We discuss the implications of this result for the economics of multidimensional screening and derive comparative statics.
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