Rationing and Common Values

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.