Don't think, that in Germany the situation is that much better. We might not have those agreements in the contracts, since in Germany there are (luckily) many regulations what can be put into contracts. But the German law has also some specialties: For example, when you make an invention in your free time, even when it has nothing to do with your current job, you must first ask your employer, if he wants to buy the invention, if you want or not.
The law in question is the Arbeitnehmererfindungsgesetz (Employee Invention law). Also, there are a few subtleties:
a) You have to do that if you intend to charge money for the invention during the time of your contract. You can quit and then start using your invention. Just don't do it while your contract is running (this avoids you building a competition to your employer).
b) The employer has to immediately patent or copyright the work and give you a compensation for licensing it.
Since you posted the same thing further upthread, I'll correct you here as well:
Actually, go read the law (ArbnErfG, § 18 Mitteilungspflicht, Satz (3)) says otherwise:
(3) Eine Verpflichtung zur Mitteilung freier Erfindungen besteht nicht, wenn die Erfindung offensichtlich im Arbeitsbereich des Betriebes des Arbeitgebers nicht verwendbar ist.
You only have to ask your employer if the invention was made in the course of your work (during work time) or part of the employers business. Totally unrelated inventions made in your free time are _not_ covered by the law.
I don't think, that you are free to set your own price. But of course, I am not current in these special law topics. But in Germany, as in many other countries: If it goes to court, you will loose against a big company.
It was an other situation, but a lawyer once told me, what happens when such things go to court: The corporation will bring 10 witnesses against you and will bring 10 experts certifying what the corporation needs.
And than you will be very alone and be gracious to get even a little money. You will loose your job anyway.
You're not free to set your own price, there are guidelines set forth in the law (ArbnErfG, § 11 Vergütungsrichtlinien) - which also means that the employer cannot undercut those guidelines and force you to hand your invention over for free. If there's a disagreement about the price, there's a mediation set forth in the law, so the first thing would not be a court case.
In general, german courts are quite employee friendly, so seriously, your employer would probably be at least as afraid to go to court as you'd be. Maybe not if it's a litigation-happy megacorp, but the bulk of german companies is medium-sized (Mittelstand) and they tend to shy away from court cases.