Allocating Multiple Units

36 Pages Posted: 30 Nov 2001

See all articles by Kala Krishna

Kala Krishna

Pennsylvania State University - Department of Economics; National Bureau of Economic Research (NBER)

Torben Tranaes

Rockwool Foundation Research Unit; Danish National Institute of Social Research (SFI); CESifo (Center for Economic Studies and Ifo Institute); IZA Institute of Labor Economics

Abstract

This paper studies the allocation and rent distribution in multi-unit, combinatorial bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points.

Note: Previously Titled "Allocating Multiple Units by Sealed-Bid Auctions"

Keywords: Menu Auctions, Multiple-Unit Auctions, First-price vs. Second-price Auctions, Revenue Equivalence

JEL Classification: D43, D44

Suggested Citation

Krishna, Kala and Tranaes, Torben, Allocating Multiple Units. Available at SSRN: https://ssrn.com/abstract=60792 or http://dx.doi.org/10.2139/ssrn.60792

Kala Krishna (Contact Author)

Pennsylvania State University - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Torben Tranaes

Rockwool Foundation Research Unit ( email )

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Danish National Institute of Social Research (SFI) ( email )

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Denmark

CESifo (Center for Economic Studies and Ifo Institute)

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Germany

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IZA Institute of Labor Economics

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