Is there are place where I can find the algorithm - or at least part of it - by which CME is computing price based on bid and ask volume and whatever other variables they include?
So, if CME does not determine price who else? To make my question more clear: There must be some computer on which a program is running that "decides" when to move bid or ask price. Obviously it is not possible (for normal traders) to make trades outside of bid/ask. So it is not any traders choice what trades happen but there is a matching algorithm running on their (CME or whereever) computers. In other words they do not just "report" trades they somehow "arrange" them.
This is the only instance of an "Algorithm" utilized to determine when price or time takes precedence. http://www.cbot.com/cbot/pub/page/0,3181,2000,00.html
The traders buying and selling determine the price and the CME reports the result. The CME just provides the market mechanism (price matching), but without traders nothing would happen. Read all you want about Globex price matching algorithms at http://www.cmegroup.com/globex/introduction/index.html and select "Matching Algorithms".
In order to open a market for the start of trading, there is an algorithm that establishes an opening range based upon the existing orders put into the system that also attempts to maximize trading volume in order to produce the fairest range. After that, completed trades influence the market.