Second Price Sealed Bid/Vickrey Auction

Published by Mario Oettler on

In the second price sealed bid (also called Vickrey Auction), bidders submit their bids in a closed envelope. So, other bidders don’t know what the highest bid is when submitting their bid. After the submission period, the auctioneer opens all envelopes, and the highest bid wins. But instead of paying the highest price, only the second-highest price needs to be paid by the winner.

The strategy for bidders is, to be honest regarding their willingness to pay (WTP). It is optimal to bid the true willingness to pay when submitting the bid because the winner only pays the second-highest price.

If a participant bids higher, he would face the risk of overpaying. And if he bids lower than his WTP, he risks that someone bids a bit higher and receives the item instead of him.

Bid open/sealedSealed
Bids increase or decreaseOnly one bit per participant
Bid orderOnly one bit per participant
WinnerBidder with the highest bid
Final priceSecond highest bid
End of auctionEnd of submission period
StrategyTell the true willingness to pay

The Vickrey Auction can suffer from collusion. A group of bidders can form a ring R. Members of this ring don’t bid individually. Only the member with the highest willingness to pay submits a valid bid. All other ring members submit invalid bids or bids that are very low and have no chance of winning.

The idea is that this increases the gap between the highest bid and the second-highest bid becomes larger. Let’s consider a numerical example:

ParticipantWillingness to Pay in EUR

This table shows the willingness to pay for each participant in the auction.

In the case of no collusion, A would win the auction and would have to pay 90 EUR. His profit would be 10 EUR (100 – 90 = 10).

Now, let’s assume that A, B, C, and E collude and become ring members. They agree on the following bidding strategy. A submits his true willingness to pay. But B, C, and E don’t submit any bids. The bids would look as follows:

ParticipantWillingness to Pay in EUR

Bids in the case of collusion among A, B, C, and E. Bidder A would win the auction, but he only needs to pay 80 EUR (instead of 90 EUR). The additional saving can be distributed among the ring members. However, distributing the saving is not trivial. Only participants B and C make a difference in the price to be paid. Participant E would not influence the price since his willingness to pay is lower than D’s.