The first mechanism they are considering is as follows. Anna and Bob simultaneously write on a piece of paper what fraction of the cake they would like to have. Then, their parents will open both envelopes. If the sum of the numbers that Bob and Anna wrote are less or equal than 1, then each of them will get the fraction of cake that they wrote down and throw away the rest. Otherwise,if the sum is greater than one, their parents will throw away the entire cake.

(a) Assuming common knowledge of rationality, what outcomes are possible in this mechanism?

(b) Is the outcome of the mechanism always Pareto efficient? (c) Do you think this mechanism is fair?