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

28 Pages Posted: 18 Mar 2019

See all articles by Santiago Balseiro

Santiago Balseiro

Columbia Business School - Decision Risk and Operations

Negin Golrezaei

Massachusetts Institute of Technology (MIT) - Sloan School of Management; Massachusetts Institute of Technology - MIT Sloan School of Management; Massachusetts Institute of Technology (MIT) - Sloan School of Management

Vahab Mirrokni

Google Inc.

Sadra Yazdanbod

Google Inc.

Date Written: February 25, 2019

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.

Suggested Citation

Balseiro, Santiago and Golrezaei, Negin and Mirrokni, Vahab and Yazdanbod, Sadra, A Black-Box Reduction in Mechanism Design with Private Cost of Capital (February 25, 2019). Available at SSRN: https://ssrn.com/abstract=3341782 or http://dx.doi.org/10.2139/ssrn.3341782

Santiago Balseiro

Columbia Business School - Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Negin Golrezaei (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Massachusetts Institute of Technology - MIT Sloan School of Management ( email )

100 Main Street
Building E62-577
Cambridge, MA 02142
United States

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Vahab Mirrokni

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

Sadra Yazdanbod

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

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