How to compete in this special scenario?

There are currently two providers of an IT-solution in a national market. These two charge roughly four times the price I would expect to see in a functioning market. This indicates that the two have set the price in cooperation. Some customers believe that the current price is a rip-off.

I could enhance the product with new features, which could make the product something like 20% better.

My question is, how should I enter the market. Should I go for the minimum viable product? Should I take the market with storm in some way? Should I put my price as high as them and just sell more aggressively?

To make it clear, my goal is simply to earn as much money as possible over a period of, say, 10 years.

Keep in mind, you're providing a better product for less, they're providing a stable long term relationship that company's have had, maybe for years (I don't know what your selling). None of the companies I've worked with like switching vendors. I read somewhere you have to be 10 times better/cheaper for someone to switch from what they're already using.

With that said, I'd be tempted to start high, you can always lower your price, it's much harder to raise it. If it's something that's web based, release early and often. Otherwise, you'll want to have as many major features as your schedule can stomach.

Some considerations:

1. Can they quickly drop their prices and match you?
2. You don't have any conflicts with this right (i.e. working for one of them or signing a contract with one of them as a vendor that prevents you from competing?)

It sounds like there might be a good opportunity there without knowing any more details.

First, determine what is the most profitable segment of your marketplace. Then set your prices and determine your required feature set accordingly. This strategy has worked quite well for companies like Apple. You don't have to beat the big guys or own the entire market to get the lion's share of the profits from a market.