Auctions: The Science of Bidding
When you try to buy or sell things at an auction, your choices depend on what other people do. Because your choices depend on their choices, math experts call auctions "games."
Auction theory belongs to Game Theory. It helps us find:
- The best way to bid so you don't pay too much
- The smartest way to set up an auction if you want to sell something
Common Auction Types
Change the rules of the game, and you change how people play. Look at these four main types:
- English Auction: This type is the most famous. Bidders call out higher and higher prices. When no one bids more, the highest bidder wins.
Tip: Stay in the game until the price hits your max limit. - Dutch Auction: High starts the price, and then it drops lower and lower. It stops the moment someone yells "Mine!"
Tip: Wait for a low price, but don't wait so long that someone else grabs it! - Sealed First-Price Auction: On a secret piece of paper, everyone writes a bid. The highest bid wins and pays that exact amount.
Tip: Bid a little less than your true value to keep some profit. - Vickrey Auction: This is a "Second-Price" auction. Everyone sends one secret bid. The highest bidder wins the item, but they only pay the second-highest price!
Example: The Vickrey Auction
Three people want to buy a beautiful painting. Here's what they think it is worth:
- Alice: Worth $500
- Bob: Worth $600
- Charlie: Worth $400
In a Vickrey auction, the best move is always to bid exactly what you think the item is worth. Let's look at the choices from Charlie's point of view:
| Charlie's Strategy | If Bob bids $550 (Highest other bid) | If Alice bids $350 (Highest other bid) |
|---|---|---|
| Bid Honestly ($400) | Charlie loses. Bob wins. Payoff: $0 |
Charlie wins, pays $350. Profit: +$50 |
| Overbid ($600) | Charlie wins, but pays $550! Profit: −$150 (Loss) |
Charlie wins, pays $350. Profit: +$50 |
| Underbid ($300) | Charlie loses. Bob wins. Payoff: $0 |
Charlie loses. Alice wins. Payoff: $0 (Missed out on profit!) |
No matter what other people bid, you get the best result when you bid your true value. In math, we call this a dominant strategy!
The Winner's Curse
To win an auction feels great, but sometimes the winner pays way too much. We call this the Winner's Curse.
When people get too excited, they forget the true value of the item. It also happens when people guess the value wrong.
Example: A Jar of Coins
Imagine a big glass jar full of coins. No one knows the exact amount of money inside. If you bid $50 to win it, but the jar only holds $30, you won the jar but lost your money. You are cursed by the win!
Real-World Uses
Airwaves Auctions
To make your mobile phone data work, phone companies need to use the airwaves. Governments sell the rights to this, through auctions worth billions of dollars!
Bad rules or bad bidding can make companies pay too much and go broke.
Internet Ads
Every time you load a webpage, a tiny, lightning-fast auction happens. In less than a second, computers bid against each other to show you ads.
Online Sellers
Some online sellers let you bid for an item. The auction can sometimes get too exciting in the last few minutes!