Multidimensional Heterogeneity and Platform Design

One of the most salient issues faced by platforms like newspapers and credit card issuers is that users are heterogeneous in the value they bring to other users or to the platform. We develop a model with multi-dimensional heterogeneity where a monopoly platform chooses (price or non-price) instruments. Users play two roles: 1) they are users of the platform’s services with heterogeneous preferences over instruments and platform characteristics; 2) they make heterogeneous contributions that endogenously determine these characteristics. The marginal (private or social) value of an instrument or characteristic includes the classical direct impact on pro?t and on (relevant) participants’ utilities, but also includes a novel sorting effect of marginal users and consequent further impact on platform characteristics. The sorting effect is quanti?ed by the covariance, within the set of marginal users, between user preferences and user contributions towards characteristics. The private optimum departs from effciency by prescribing lower quantities and catering to the tastes of marginal (rather than average) users. Under reasonable conditions, optimal allocations may be implemented uniquely by allowing each instrument to be contingent on all characteristics. We discuss applications to newspapers, broadcast media, credit cards, and suggest simple extensions to the case of imperfect competition in insurance provision and college admissions.