- Examples of auction-type markets
Examples of auction-type markets include Sotheby's in London, who auction fine art, collectibles, and antiques. Another example of an auction-type competitive market would be the Barrett-Jackson auto auctions in America, where luxury and muscle cars are displayed and auctioned off for high profits.
Auction-based marketplaces can be subject to fluctuations that are affected by stock market conditions and other issues - if the economy is rough, people may not be willing to go out on a limb bidding high for something they want. Auction-type marketplaces can also be for ordinary things, such as cattle or other livestock, or fish - in fact, there are many fish markets that use auctioning to sell huge tunas for thousands of dollars!
- Perfect competition?
Another type of market is really more of a concept than anything else - a perfect competition market is sort of a "dream" situation where every person who contributes to the marketplace is not too powerful; in other words, no one has too much control over the whole system, so no one can dominate or destroy anyone else.
In real life, you don't see evidence of perfect competition too often - if you see it at all. Maybe the Communists in Russia tried to put perfect competition into effect by making sure all things were shared equally between the people, but all this did was trigger a whole separate, underground economy, known as a "black market".
To learn more about competitive markets, read some macro and micro economics - you can take courses on this subject matter, or pick up a book on the subject. Competitive markets are also examined in the financial pages of most newspapers.