Cutting cakes
There is a great mechanism in tabletop games called "I cut, you choose", also known as "I split, you choose", which creates a very interesting dynamic. The mechanism is based on the method used by two people to fairly divide something - let's say a cake. One person cuts the cake into two slices. That person can decide to make one slice bigger than the other, but it's the other person who chooses which slice they want. So if the cutter makes one slice bigger than the other, the chooser can decide to just take the bigger slice, which of course encourages the cutter to make both slices equal.
