Rationing and Common Values

GSIA Working Paper No. 2001-E7

32 Pages Posted: 9 Jun 2001

See all articles by Christine A. Parlour

Christine A. Parlour

University of California, Berkeley - Finance Group

Uday Rajan

Stephen M. Ross School of Business, University of Michigan

Date Written: June 8, 2001

Abstract

We consider a rationing mechanism for selling a common-value object, in which the seller solicits sealed bids, and allocates the objects with equal probability to one of the k highest bidders, at the (k+1)th highest price. When k > 1, this mechanism exhibits rationing. When k=1, it reduces to the second-price auction, or market-clearing. The mechanism is formally equivalent to dividing the object into k units, and allocating 1/k units to each of the k highest bidders, at the (k+1)th highest price, for some k > 1. When the prior over true value is uniform, we characterize the bid and revenue functions, and determine a necessary and sufficient condition for revenue (conditional on true value) to increase with rationing. We show that this condition is satisfied when the signal distribution is diffuse, and that rationing is less attractive when signals are relatively precise. In the presence of a liquid secondary market, financial assets are reasonably modelled as having common values. Rationing is commonly observed in IPOs, and this result suggests that it may be superior to allocating the shares at a market-clearing price.

Keywords: common value auctions, rationing, winner's curse, IPO's

JEL Classification: D44, G2

Suggested Citation

Parlour, Christine A. and Rajan, Uday, Rationing and Common Values (June 8, 2001). GSIA Working Paper No. 2001-E7, Available at SSRN: https://ssrn.com/abstract=272814 or http://dx.doi.org/10.2139/ssrn.272814

Christine A. Parlour (Contact Author)

University of California, Berkeley - Finance Group ( email )

Haas School of Business
545 Student Services Building
Berkeley, CA 94720
United States
510-643-9391 (Phone)

Uday Rajan

Stephen M. Ross School of Business, University of Michigan ( email )

701 Tappan Street
Ann Arbor, MI 48109
United States
734-764-2310 (Phone)

HOME PAGE: http://webuser.bus.umich.edu/urajan

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