Capitulation is the act of surrendering or giving up. If you enter a pie eating contest when you're already full, you'll probably have to end up in a state of capitulation.
The original meaning of capitulation is "the formal terms of surrender between governments." The word comes from the Latin capitulāre, with a root in capital, or "the head of state." You can use capitulation for any act of surrender. If you're stuck in an endless argument with your neighbor over the exact boundary between your properties, only the original deeds to the land will bring about a capitulation.