Dynamic Mechanism Design with Budget Constrained Buyers Under Limited Commitment

89 Pages Posted: 22 Jan 2016 Last revised: 2 Nov 2018

See all articles by Santiago Balseiro

Santiago Balseiro

Columbia Business School - Decision Risk and Operations

Omar Besbes

Columbia Business School - Decision Risk and Operations

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University; Columbia University - Columbia Business School - Decision Risk and Operations

Date Written: September 18, 2018

Abstract

We study the dynamic mechanism design problem of a seller that repeatedly auctions independent items over a discrete time horizon to buyers that face a cumulative budget constraint. A driving motivation behind our model is the emergence of real-time bidding markets for online display advertising in which such budgets are prevalent. We assume the seller has a strong form of limited commitment: she commits to the rules of the current auction but cannot commit to those of future auctions. We show that the celebrated Myersonian approach that leverages the envelope theorem fails in this setting, and therefore, characterizing the dynamic optimal mechanism appears intractable. Despite these challenges, we derive and characterize a near-optimal dynamic mechanism. To do so, we show that the Myersonian approach is recovered in a corresponding fluid continuous time model in which the time interval between consecutive items becomes negligible. Then, we leverage this approach to characterize the optimal dynamic direct-revelation mechanism, highlighting novel incentives at play in settings with buyers' budget constraints and seller's limited commitment. We show through a combination of theoretical and numerical results that the optimal mechanism arising from the fluid continuous time model approximately satisfies incentive compatibility for the buyers and is approximately sequentially rational for the seller in the original discrete time model.

Keywords: dynamic mechanism design, limited commitment, budget constraints, fluid approximation, display advertising, internet auctions, revenue management

Suggested Citation

Balseiro, Santiago and Besbes, Omar and Weintraub, Gabriel Y., Dynamic Mechanism Design with Budget Constrained Buyers Under Limited Commitment (September 18, 2018). Columbia Business School Research Paper No. 16-10. Available at SSRN: https://ssrn.com/abstract=2720355 or http://dx.doi.org/10.2139/ssrn.2720355

Santiago Balseiro (Contact Author)

Columbia Business School - Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Omar Besbes

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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