Auctions: The Science of Bidding
Auction Theory is part of Game Theory. It looks at how people act when they try to buy or sell things in an auction.
In a game, what you do depends on what others do. This is why we call auctions "games." Let's look at:
- Best ways to bid so you don't pay too much
- Smart ways to set up an auction if you are the seller
Common Auction Types
The rules of the game change how you play. Here are the four main types:
- English Auction: This is the most famous kind. Bidders call out higher and higher prices. When no one bids more, the highest bidder wins.
Tip: Stay in until the price hits your limit. - Dutch Auction: The price starts very high. It drops lower and lower until someone says "Mine!"
Tip: Wait for a low price, but don't wait so long that someone else grabs it first! - Sealed First-Price Auction: Everyone writes their bid on a secret slip of paper. The highest bid wins and pays that exact price.
Tip: Bid a little less than you think it is worth, to keep some profit. - Vickrey Auction: This is a "Second-Price" auction. Everyone sends a secret bid. The highest bidder wins, but they only pay the second-highest price
Example: Vickrey Auction
In a Vickrey auction, the highest bidder wins but pays the second-highest bid price.
There's a beautiful painting up for auction:
- Alice: Valuation $500, Bids $450
- Bob: Valuation $600, Bids $550
- Charlie: Valuation $400, Bids $600 (Overbidding)
Analysis: If Charlie bids $600, he wins because he is the highest bidder. However, he pays Bob's bid ($550). Since Charlie only values the painting at $400, his payoff is -$150.
*But had Charlie bid $400, he would have lost the auction, a better choice!
This shows that overbidding in a Vickrey auction is a losing strategy.
The Winner's Curse
The Winner's Curse is when you win an auction but pay way more than it is worth!
This can happen when people get excited or don't know the true value of what they are buying.
Example: The Jar of Coins
Imagine a jar full of coins. You don't know how much money is inside. If you bid $50 to win it, but the jar only has $30 inside, you have been "cursed" by the win!
Real-World Uses
Government Spectrum Auction
Governments sell "airwaves" to phone companies so your mobile data works. These auctions involve billions of dollars! If the rules are bad, the companies might overpay and go broke.
Internet Ads
Every time you see an ad on a website, a tiny, super-fast auction just happened. Computers bid against each other in milliseconds to show you that ad.
Main Idea: Auctions use math to make sure things go to the people who want them most for a fair price.