# Vickrey Auction

A sealed-bid auction where participants submit bids without knowing the bids of others, with the second-highest bid winning the auction

## What is a Vickrey Auction?

A Vickrey auction is a sealed-bid auction where bidders submit bids without knowing the bids of other people. However, as opposed to other sealed-bid auctions, the price paid is the second-highest bid price and not the winning bid price. The Vickrey auction was named after William Vickrey, a Canadian who won the 1996 Nobel Prize in Economics for his research on asymmetric information in economics.

### Understanding a Vickrey Auction

In a Vickrey auction, the individual is bidding their true value and are not trying to assess what everyone else is going to bid. Therefore, in a Vickrey auction, the individual is bidding the maximum amount they are willing to pay and are not disadvantaged by it.

By utilizing the second-price mechanism in a Vickrey auction, individuals bid truthfully – individuals are motivated to bid their maximum value because the individual understands that if their bid wins, they will only need to pay the second-highest bid value.

For example, consider an auction for an antique to which an individual places a \$100 value on.

1. The individual would not post a higher bid than the maximum value (\$100) he has established for the antique due to the possibility of having to pay a price higher than his maximum willingness to pay of \$100.
2. The individual would not post a lower bid than the maximum value (\$100) he has established for the antique due to the possibility of losing the antique for a price less than the maximum amount the individual is willing to pay.

### Example of a Vickrey Auction

There are six individuals involved in a Vickrey auction for an antique. Each individual bids their maximum willingness to pay for the antique, as illustrated below. Under a Vickrey auction, who will win the auction and what will the price paid for the antique?

Individual A will win the auction due to his highest bid of \$103. However, Individual A does not pay the highest bid price – he pays the second-highest bid price. In our example, he will only need to pay \$101. Therefore, Individual A’s maximum willingness to pay is \$103, and he only ends up paying \$101 for the antique – a \$2 surplus.

### Vickrey Auction: Bid Higher or Bid Lower?

We can extend the example above to understand whether individuals will make a bid higher than their willingness to pay. Recall that in a Vickrey auction, there is no incentive to bid a price higher or lower than the bidder’s maximum willingness to pay. For example:

#### Bidding Higher Than Maximum Willingness to Pay?

If Individual B’s maximum willingness to pay is \$101, and he bids \$105, he runs the risk of having to pay a higher price than his willingness to pay (this is a risk because it would only occur if the first runner-up’s bid is higher than the individual’s maximum willingness to pay).

In such a case, the first runner-up will be Individual A at a price of \$103 – a \$2 deficit from Individual B’s maximum willingness to pay.

#### Bidding Lower Than Maximum Willingness to Pay?

If Individual A’s maximum willingness to pay is \$103 and places a lowball bid of \$100, he runs the risk of losing the bid at a price that the individual would’ve been willing to pay (it is a risk because it will only occur if another bidder places a bid that was higher than the lowball offer).

In such a case, Individual B will end up winning the auction at \$101 and only need to pay Individual C’s price of \$100.50. If Individual A lowballs the offer, he ends up losing the bid, and the winner only needs to pay \$100.50 – less than what Individual A would’ve paid.

### Key Takeaways

In a Vickrey auction, bidders are unaware of the bids of other individuals. The winner of the bid does not pay the winning bid price – the individual pays the second-highest bid price.

In such an auction, individuals are encouraged to bid their maximum willingness to pay. In the absence of collusion, there is no incentive for an individual to bid higher or lower than their maximum willingness to pay.

### More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful:

• Dutch Auction
• English Auction
• Forced Sale Value
• Targeted Auction

### Financial Analyst Certification

Become a certified Financial Modeling and Valuation Analyst (FMVA)® by completing CFI’s online financial modeling classes and training program!