Complete games with minimum

Some real-world examples of simple games, like the procedure to amend the Canadian Constitution, are complete simple games with minimum. Using characteristic invariants for this class of games, we study different types of solution concepts. For an arbitrary number of players we get the nucleolus by means of a determinate compatible system of equations, characterize the maximality of the kernel and give a method to calculate semivalues. Several applications are found at the end of the paper.