First, what you forget is that roads are not the only means of transportation. Such a road company would not be able to raise prices indefinitely because customers would either switch to air travel, river transport, or, I don't know, hyperloops, or stop using the road completely. Now what it could do is find the equilibrium price at which customers are still willing to use the road and not switch to a competitor. That might seem like a problem, because the prices would still be higher, but then you have to think back to the time when this project was conceived.

Imagine you are an investor who wants to build that important tunnel. If there is a demand, obviously you wouldn't be the only one. So each of you, investors, would come up with offers for the potential customers for this road. The one who offers the best conditions - for instance, fixed low price for the next 10 years - gets the most customers and proceeds on building that tunnel. If that investor later decides to cheat and raises prices then he would have to deal with law firms of his customers, which would potentially be costly.

So here you see how this potentially difficult situation can be resolved without the need for any government whatsoever.