The currency obviously has been given it's value somehow. I know it is preached to be different than regular fiat currency, but I am very curios how it went from an idea to now being able to be used for purchases, and given a value in relation to USD.

Me and a group of friends cannot come up with an idea for something to be used for transactions and then have that idea be able to transform into a countries currency. We can trade amongst ourselves but there is no way we can give it a value to be used to trade it into dollars. There has to be some type of government involvement in order for bitcoin to have a value in relation to a nations currency.

My question is how is the original concept of bitcoin given a value in dollars? Does this mean there is significant government involvement in bitcoin?