This question already has an answer here:
For the fair cutting of a cake into n pieces for n people, is it sufficient for one person to cut the cake, and for them to get the last pick of piece?
If any one piece is bigger than 1/n, another person will take that piece. If any one piece is smaller than 1/n, then the cutter may end up with that piece. Therefore the cutter has an incentive to cut the cake fairly.
Is this correct?