Math Fun Facts!
hosted by the Harvey Mudd College Math Department created, authored and ©1999-2010 by Francis Su
Subscribe to our RSS feed   or follow us on Twitter.
Get a random Fun Fact!
No subject limitations
Search only in selected subjects
    Calculus or Analysis
    Number Theory
    Other subjects
  Select Difficulty  
Enter keywords 

  The Math Fun Facts App!
  List All : List Recent : List Popular
  About Math Fun Facts / How to Use
  Contributors / Fun Facts Home
© 1999-2010 by Francis Edward Su
All rights reserved.

From the Fun Fact files, here is a Fun Fact at the Medium level:

Vickrey Auction

Suppose you are hosting a silent auction to sell your antique car. The rules are: (1) prospective buyers bid for your car by placing their bids in sealed envelopes, (2) then after collecting all bids, you sell the car to the highest bidder for the price that he bid.

This may seem like a reasonable way to conduct a silent auction, but there is a risk involved for you, the seller. If your car is highly valuable, but all buyers think they are the only ones who recognize that it is, they may actually make bids that are LESS than they think the car is actually worth. As a result, your bids will be lower, and you suffer.

Are there rules for a silent auction that will induce people to bid what they think an object is truly worth?

The answer is yes, and is given by a Vickrey auction. The rules specify that each player make bids, and the car goes to the highest bidder, but at the second-highest bid!

Can you figure out why this induces people to bid truthfully?

Presentation Suggestions:
This may be fun for students to ponder, or try as a group experiment, before discussing the answer. Additionally, you could ask students to think about what behavior other kinds of bidding rules would induce.

The Math Behind the Fact:
Here is the reason it works--- we'll show that, when holding all other bids fixed (and unknown to a given bidder), that bidder's optimal strategy is to bid what she thinks the car is worth.

Suppose the bidder's name is Alice. Let V be the amount that Alice thinks the car is actually worth, and B the bid that she actually makes. Let M be the maximum of all other bids. If M is more than V, then Alice should set her bid B less than or equal to V, so that she does not get the car for more than she thinks it is worth. If M is less than V, then Alice should set B=V, because if she bids any less, she will not get the car any cheaper, and she may lose the car.

The study of mathematical models for decision making is called game theory.

How to Cite this Page:
Su, Francis E., et al. "Vickrey Auction." Math Fun Facts. <>.

Keywords:    game theory
Subjects:    other
Level:    Medium
Fun Fact suggested by:   Francis Su
Suggestions? Use this form.
Click to rate this Fun Fact...
    *   Awesome! I totally dig it!
    *   Fun enough to tell a friend!
    *   Mildly interesting
    *   Not really noteworthy
and see the most popular Facts!
New: get the MathFeed iPhone App!

Brings you news and views on math:
showcasing its power, beauty, and humanity

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!