If an entity is large and powerful enough, is it possible for it to gain a monopoly advantage and manipulate the rises and falls of the virtual currency market?
Yes, big whales are already doing it. In my opinion, it is harder in case of bitcoins as it is old and there are many investors who got involved when crypto was in early stages and whales were not noticing this.
Trying to manipulate bitcoin is getting harder but only if you are holding fiat since bitcoin is getting more expensive after each year, but if you are holding a lot of bitcoins and whales do, then it is easy to manipulate the price, if you want to make the price to go down you only need to sell some of your coins when there is a strong FUD and the market will crash and then the whales can get cheap coins after the market reaches the bottom.