A lot of the market movement is caused by people setting fixed prices on their transactions. Eg: Sell 5 BTC at X Or buy 5 BTC at Y. If X or Y is never reached the transaction never takes place.
Generally the exchanges just connect a buyer to a seller. You are not buying the exchanges coins but rather the coins of another individual/trader. The exchanges are just middle men facilitating the sale.
The exchanges make money on a per transaction basis on fees. If the market grinds to a halt because there are no transactions the exchanges make no money.
Now there are many possible reasons for the recent spike, some malignant such as potential pump n dump scheme or artificial inflation due to the upcoming futures exchanges and the desire to profit from shorting and some benign such as all the media attention and fear of missing out or just genuine belief in the potential of BTC as a currency or asset.
No idea which reason is accurate, could be all of them or none.
So to give you a little more info: 1) Yes, there are big players (aka "whales"), and the rest of the "small fish", all playing in the same pond. The interesting thing about cryptos is that the are more "money-like" than "stock-like" when it comes to trading. Meaning just like money, where I can buy a fraction of a $, I can also buy a fraction of a bitcoin. So there are a lot of smaller players who will buy, say .01 BTC for $150 right now.
But while there is a general consensus that bitcoin is $15k by virtue of people paying that much for it, the "whales" (people with a lot of money or coins), can cause issues because they can put a lot of volume on or take a lot of volume off the order book at once. This happened to Ether this year, dumping the price for a few minutes from >$300 down to about 10 cents for a few minutes! https://blog.gdax.com/eth-usd-trading-update-5d8142b5bdc1
In fact, there is some speculation that a lot of the rise right now is from Wall St. / big firms buying up a lot of coin, as futures trading on Bitcoin is coming in the coming weeks! (But I don't know enough to comment on that theory)
As far as preventing exchanges themselves from colluding... it would be difficult but not impossible, because again the price on the exchanges comes from the traders, not the exchanges themselves. (Theoretically it is possible that an exchange could do a bunch of "wash trading" / make up a bunch of fake trade volume to make demand look higher than it was, but given that there are a number of exchanges in a number of different countries, coordination there might be difficult)
We don't really know.
>Or is there a general consensus that the price is $15K. And wouldn't there have to be people that we willing to pay this price? What prevents the exchanges from colluding and raising the price artificially?
Well the exchanges could be running buy-bots but I think the more likely collusion is going to be big-players selling to themselves, if a big player is filling up both sides of the order book they can make it look like there is a lot of activity and drive the price up that way. Now is this that or is it organic? I'm not sure we have a good way to tell.