On Optimal Auctions for Mixing Exclusive and Shared Matching in Platforms

Platforms create value by matching participants on alternate sides of the marketplace. Although many platforms practice one-to-one matching (e.g., Uber), others can conduct and monetize one-to-many simultaneous matches (e.g., lead-marketing platforms). Both formats involve one dimension of private information, a participant's valuation for exclusive or shared allocation, respectively. This paper studies the problem of designing an auction format for platforms that mix the modes rather than limit to one and, therefore, involve both dimensions of information. We focus on incentive-compatible auctions (i.e., where truthful bidding is optimal) because of ease of participation and implementation. We formulate the problem to find the revenue-maximizing incentive-compatible auction as a mathematical program. Although hard to solve, the mathematical program leads to heuristic auction designs that are simple to implement, provide good revenue, and have speedy performance, all critical in practice. It also enables creation of upper bounds on the (unknown) optimal auction revenue, which are useful benchmarks for our proposed auction designs. By demonstrating a tight gap for our proposed two-dimensional reserveprice-based mechanism, we prove that it has excellent revenue performance and places low information and computational burden on the platform and participants.