Quantifying the Inefficiency of Multi-unit Auctions for Normal Goods

36 Pages Posted: 31 Aug 2021

See all articles by Brian Baisa

Brian Baisa

Amherst College

Simon Essig Aberg

affiliation not provided to SSRN

Date Written: August 27, 2021


We study multi-unit auctions for homogenous goods in a private value setting where bidders have non-quasilinear preferences. Several recent impossibility results study this setting and find there is no mechanism that retains the Vickrey auction’s desired incentive and efficiency properties without quasilinearity. While a fully efficient mechanism is impossible, we show that any undominated outcome of the Vickrey auction has a negligible inefficiency when bidder wealth effects are sufficiently small. In order to show this, we first place bounds on undominated bid behavior in the Vickrey auction when bidders have non-quasilinear preferences. We use (Marshallian) deadweight loss as our inefficiency metric, and we derive a tight upper bound on the inefficiency associated with the Vickrey auction in terms of the degree of bidder wealth effects. As wealth effects diminish, the bound continuously approaches zero. Other common multi-unit auction formats do not have this property, and their worst-case inefficiencies are higher than that of the Vickrey auction.

Keywords: Undominated actions, wealth effects, multi-unit auctions, non-quasilinear preferences, Pareto efficiency.

JEL Classification: D44, D47, D61, D82.

Suggested Citation

Baisa, Brian and Essig Aberg, Simon, Quantifying the Inefficiency of Multi-unit Auctions for Normal Goods (August 27, 2021). Available at SSRN: https://ssrn.com/abstract=3912928 or http://dx.doi.org/10.2139/ssrn.3912928

Brian Baisa (Contact Author)

Amherst College ( email )

Amherst, MA 01002
United States

HOME PAGE: http://https://www.amherst.edu/people/facstaff/bbaisa

Simon Essig Aberg

affiliation not provided to SSRN

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