Multidimensional Sequential Screening

TL;DR

This paper analyzes how a monopolist can optimally design multidimensional sequential screening mechanisms, revealing conditions under which separate sales for each good are optimal, thus explaining common practical practices.

Contribution

It characterizes the optimal multidimensional screening mechanism, showing when separate sequential screening for each good is optimal under certain distributional conditions.

Findings

Optimal mechanism frontloads surplus extraction before valuations are realized.

Under FOSD ordering and invariant dependencies, separate screening for each good is optimal.

The results justify common practice of membership payments followed by separate sales.

Abstract

I study multidimensional sequential screening. A monopolist contracts with a buyer who privately observes information about the distribution of their eventual valuations for multiple goods. After initial private information is reported and the contract is signed, the buyer learns and reports realized valuations. In these settings, the monopolist frontloads surplus extraction: Any information rents given to the buyer to elicit their true valuations can be extracted in expectation before those valuations are drawn, transforming the multidimensional screening problem by distorting buyer information rents compared to static screening. If the buyer's distributions over valuations are commonly FOSD ordered, regular for each good, and satisfy invariant dependencies (valuations can be dependent across goods, but how valuations are coupled cannot vary), the optimal mechanism coincides with independently offering the optimal sequential screening mechanism for each good. This rationalizes membership payments followed by separate sales schemes commonly used in practice.