Information design of matching platforms when user preferences are bidimensional

Companies that provide a two‐sided platform for users to proactively seek a match face great challenges in increasing matching efficiency and ensuring match quality. This paper examines how information designs can be used to improve matching outcomes when users derive utility from a match's vertical attribute (i.e., quality) and its horizontal attribute (i.e., idiosyncratic fit). We consider a game‐theoretic model in which competing senders propose matching requests to competing receivers and users on the two sides are differentiated both horizontally and vertically. We first demonstrate that users' preference for the vertical attribute intensifies competition and hurts matching efficiency, and to avoid competition a sender may switch from a close receiver to a distant receiver even when the weight that he places on a match's horizontal closeness increases. Second, we examine four information designs in which one type of information from one side of the market is withheld. Designs that withhold either side's vertical information increase the number of matches, with the improvement from withholding receivers' information being greater. By contrast, designs that withhold either side's horizontal information can cause all requests to concentrate on one receiver and lead to the most severe match failure. Third, an increase in matching volume comes at the expense of certain users' welfare, as withholding one side's vertical information can hurt not only high‐quality users on both sides but also the low‐quality users on the opposite side. Although withholding one side's horizontal information may increase the matching volume under certain conditions, it can be Pareto dominated by a design that withholds one side's vertical information. Fourth, when strategic user pricing is involved, it not only redistributes user welfare but also corrects for matching distortion. Finally, in contrast to the result when strategic pricing is absent, when strategic pricing is present the platform withholding one side's vertical information can benefit all users on the opposite side, while withholding one side's horizontal information can benefit all users on the same side.