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Nobel Prize: The Quest for the Perfect Auction - Edition 2

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Last week I started to re-count an overview of the Nobel Prize for Economic Sciences 2020, with this year’s Laureates, Paul Milgrom and Robert Wilson, addressing auction theory.

The complexity surrounding auctions and a fact that makes them so engaging is that a bidder’s strategy usually depends on how he or she believes the other participants will bid during the auction. Naturally some bidders believe a property is worth more or less than others? These different views will reflect a number of influences including that some bidders may have better information about a property’s varied characteristics and so its value.

Private Values

The 1996 Laureate in Economic Sciences, William Vickrey, established auction theory in the early 1960s. He analysed a special case, in which the bidders only have private values for the good or service being auctioned off. This means that the bidders’ values are entirely independent of each other.

For instance, this could be a charity auction for dinner with a celebrity (say a Nobel Laureate). How much you are willing to pay for such a dinner is subjective – your own valuation is not affected by how other bidders value the dinner.

So how should you bid in this type of auction? You should not bid more than the dinner is worth to you. But should you bid lower, perhaps getting the dinner at a lower price?

Vickrey showed that the best-known auction formats – such as the English and the Dutch – give the same expected revenue to the seller, provided that all bidders are rational and risk neutral.

Common Values

Entirely private values are an extreme case. It’s worth recalling that most auctions, including property, are ‘public’ auctions and so they have a considerable common value. Which means that part of the value is equal to all potential bidders, they may see the location and type of property as meeting a common shared and understood value.

However, in practice, bidders also have very different amounts of private information about a property. That may be driven by very different motivations to buy and this can include emotional values.

An example. Imagine that you are a potential buyer looking at a property that’s ripe for renovation and that you, and other potential buyers are contemplating a bid for the property, so you carry out renovations and pocket considerable ‘added-value’.

Your willingness to pay an amount to secure the property at auction mainly depends on the resale value after the renovations are done. Different buyers will have different and at times very different opinions about end value, depending on everyone’s experience and what they have learned through the time spent researching the property and renovation project.

You could assess the value better if you had by some means access to the estimates of all the other bidders, but naturally each bidder prefers to keep their information secret right up until the time they bid or do not bid.

Bidders in auctions with common values and aspirations run the risk of other participants having better information (having done their homework in more detail) about the true value.

This can lead to a number of well-known and opposite phenomenon, with low bids and over-reserve high bids leading to buyer’s or seller’s remorse. Say that your bid wins at an auction, this means that the other bidders value the property less than you do, and you may, however, have better (private) information to justify your bid or your emotions may have simply carried the day.

In three classic papers from the 1960s and 1970s, Robert Wilson was the first to create a framework for the analysis of auctions with common values, and to describe how bidders behave in such circumstances, describing the optimal bidding strategy for a winning auction bid when ‘true’ value is uncertain.

Bidders will usually bid lower than their best estimate of the value, to avoid making a bad deal. Wilson’s analysis also shows that faced with greater uncertainty, bidders will be more cautious, and the final price will be lower. Finally, Wilson shows that the problems caused by buyer’s remorse are even greater when some bidders have better information than others.

Those who are at an information disadvantage will then bid even lower or completely abstain from participating in the auction, as they feel at a disadvantage.

Both Private and Common Values

In most (public) auctions, the bidders have both private and common values and information.

For example if you were thinking about bidding at auction for an apartment; your willingness to pay will mainly depend upon your private value (how much you appreciate its condition, floor plan and location) and your estimate of the common value (how much you might be able to sell it for in the future).

According to some published background related to this year’s Nobel prize; analysing bids in auctions with private and common values turned out to be a trickier problem than the special cases analysed by Vickrey and Wilson. The person who finally cracked this was Paul Milgrom, in some papers published around 1980.

Milgrom’s analysis – partly with Robert Weber – included new and important insights about auctions. One concerns how well different auction formats work. In the familiar English auction (mainly associated with property), the auctioneer starts with a low price and raises it. Bidders who observe the price at which others drop out therefore obtain information about their perception of value; as the remaining bidders then have more information, and they are less prone to bid below their estimated value and possibly miss-out. Observing others bid at the auction informs their bids.

This result reflects a general principle: an auction format provides higher revenue, with a stronger link between the bids and the bidders.

Therefore, vendors and their real estate agents have an interest in providing as much information as possible about a property’s value and potential before the auction. For example, this suggests that a vendor can expect a higher final price if the bidders have access to for example, an (independent) expert valuation and other relevant details, such as new infrastructure and more.

Auctions are a live test of value and demand for property, (and as outlined in the Nobel Prize papers, many other items and services), almost in real-time however, circumstances around values are complex. Nonetheless auctions are a robust and it would appear very fair way to arrive at a tested and fair ‘market value’.

PAUL R. MILGROM
Born 1948 in Detroit, USA. Ph.D. 1979 from Stanford University, Stanford, USA. Shirley and Leonard Ely, Jr. Professor of Humanities and Sciences, Stanford University, Stanford, USA.

ROBERT B. WILSON
Born 1937 in Geneva, USA. D.B.A.1963 from Harvard University, Cambridge, USA. Adams Distinguished Professor of Management, Emeritus, Stanford University, Stanford, USA.