Thursday, April 21, 2016

The Linkage Principle Revisited

In class, I mentioned that a firm is better off committing to release appraisals of products to be auctioned rather than remaining silent. Here's some more intuition:

Consider a situation where there is a single object of unknown value. God draws the value from some distribution, but keeps it a secret. Instead, everyone, including the auctioneer, gets an unbiased signal about the value. Think of the auctioneer's signal as his appraisal of the value of the object.

(This is sometimes called the mineral rights auction model since it can model a situation where bidders are bidding for a mine with unknown content. The ore extracted from the mine is sold at the same market price regardless of the winning bidder.)

If no appraisal is released, then bidders will bid, accounting for the winner's curse. Bids will of course differ, depending on the signal, and will, in general split the surplus between the bidders and the auctioneer.

To see the linkage principle at work, suppose the appraisal perfectly reveals the true value of the item. Now the perceived value of the item will be identical for all bidders, and everyone will simply bid the value of the item. Bidders will get no surplus and the auctioneer all of the surplus, an ideal situation for the auctioneer.

When the appraisal is an imperfect signal of value, the same basic effect applies: Bidders' perceived value for the item will be more tightly correlated, so competition will be fiercer. This makes the auctioneer better off.

Commitment is important though. If the auctioneer selectively reveals appraisals, displaying them only when they are high and not when they are low, the analysis is no longer so clean because the absence of an appraisal will now affect bidders' perceived valuations as well.

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