A Black-Box Reduction in Mechanism Design with Private Cost of Capital

Abstract

We consider a setting in which potential buyers of an indivisible item have private and heterogeneous valuation and cost of capital. The valuation and cost of capital can be correlated with each other, but they are independent across buyers. In such a setting, a buyer's utility for the item is his valuation minus his investment cost where the investment cost is the payment for the item adjusted by the cost of capital. The cost of capital allows us to model financially constrained buyers who either borrow capital to make an investment or allocate capital across multiple projects (items). We derive the revenue- and welfare-maximizing auctions under this setting by providing a reduction from a two-dimensional mechanism design problem to a single-dimensional mechanism design problem with quasilinear buyers. We show that our reduction can be extended to multi-unit environments with demand and capacity constraints as well as general matroid environments. Our work thus presents an alternative view on modeling financial constraints. Costs of capital serve as a proxy for enforcing budget constraints "softly,'' which unlike hard budget constraints, lead to tractable mechanism design problems.