This is a very interesting topic, unfortunately there are much low-quality posts.
The reason for existing a "unanimous" price across exchanges is in fact the result of arbitrage, but not only.
But why does the price move? Why does there even exist a price for a digital "good" like Bitcoin? That's the interesting question.
There are many influences:
- The prices in the past. People get a "feeling" where the price "should be" when they see the current or past price movements. That's the same thing like when you say, "a coffee must cost 2 dollars". (more precisely, "a dollar is half of a coffee")
- Future expectations. Many people hope that Bitcoin will be worth more, so they think the price could go up and buy when they see a "good opportunity". That drives the price up. Similarly, "bears" can drive the price down. The balance between these two forces is determined by the "sentiment" - it can be positive or negative.
- Large market participants. That's what some are referring as "the cartel". I don't think there is ONE cartel, but there are definiely large players that try to influence the price with their own buys and sells.
- Real world usage. The more participants the Bitcoin community has, the higher the price.
- Speculation and technical analysis. Speculators try to find patterns and react to it, driving the price up or down.
- Newly generated supply from miners. The significance is low (mined coins make up about 1 to 3 % of all sold coins), but it exists.
These are only a few factors, but I think they're the most important.The problem is that it's difficult to predict how they work together. So there is no "safe" way of guessing the "right price" or a "price trend", but you can make estimations mainly based on the "sentiment".
remenber MT Gox's Willy bot
fake transactions, fake volume. MTgox had over 75% from market at that time; China has over 90% at this time