Dynamic Mechanisms with Martingale Utilities

57 Pages Posted: 11 Aug 2016 Last revised: 28 Nov 2017

See all articles by Santiago Balseiro

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations; Google Research

Vahab Mirrokni

Google Research

Renato Paes Leme

Google Inc.

Date Written: November 27, 2017


We study the dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across multiple initial auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in earlier auctions in exchange for higher utility in later auctions. To address this problem, we introduce a martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose loss in profit with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor.

Keywords: dynamic mechanism design, martingales, approximations, dynamic auctions, internet advertising, revenue management

JEL Classification: C73, D82, D44

Suggested Citation

Balseiro, Santiago and Mirrokni, Vahab and Paes Leme, Renato, Dynamic Mechanisms with Martingale Utilities (November 27, 2017). Available at SSRN: https://ssrn.com/abstract=2821261 or http://dx.doi.org/10.2139/ssrn.2821261

Santiago Balseiro (Contact Author)

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

3022 Broadway
New York, NY 10027
United States

Google Research ( email )

Vahab Mirrokni

Google Research ( email )

Renato Paes Leme

Google Inc. ( email )

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

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