Thursday, April 21, 2016

Choosing Auctions

The revenue equivalence theorem identifies conditions where the type of auction is irrelevant to seller revenues. But how should one choose between auction forms when these conditions do not hold?

Open versus Closed

An open auction, an English auction for example, has the property that bidders can adjust their bids to others in a dynamic fashion. In a closed auction, bids are sealed. An open auction is another way to achieve linkage. If bidders' values are correlated, as in the mineral rights model, then, on average, the seller earns more from an open than a closed auction. The reason is that others' bids reveal information, much like an appraisal. This more tightly correlates perceived values and intensifies competition, an effect absent in a closed auction.

So why are closed auctions run? There are several reasons.
1. Cheating: It is easier to engage in bid rigging in an open auction since the bids of others in the ring can be monitored, and countered, if someone decides to deviate.
2. Liquidity: An open auction requires people to participate at a specific time and place. This could reduce the number of bidders attracted to the auction, leaving the auctioneer worse off.

High Bid versus Second Price

A high bid auction is simpler for bidders to understand, even if the equilibrium bidding strategy turns out to be more complex. It is also less subject to the problem of shill bidding, bids made by the auctioneer to boost the price of the item. Second-price auctions invite shill bidding, especially when it is hard to verify who placed what bids.

On the other hand, bidding in the second price auction is simpler, once it is explained. It is more robust to errors on the part of other bidders. Finally, optimal bidding in the first price auction requires knowledge of the number of competing bidders. In the second-price, it does not. For inexperienced bidders, the lack of knowledge about the level of competition, and hence the right amount of bid shading to engage in, represents a serious entry barrier.

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.