Suppose Players 1, 2, and 3 View a Cake as Shown

Essay

Suppose players 1, 2, and 3 view a cake as shown below and that all cuts are vertical. Illustrate the envy-free procedure for n = 3 (yielding an allocation of part of the cake) by following the steps below:
a) Provide a total of three drawings to show how each player views a division of the cake by player 1 into three pieces he or she considers to be the same size or value. Label the pieces A, B, and C.
b) Redraw the picture from player 2's view and illustrate the trimmings of piece B that he or she would do. Label the trimmed piece $B ^ { \prime }$ and the actual trimmings T.
c) Indicate which piece each player would choose (and what he or she thinks its size is) if the players choose in the following order: player 3, player 2, player 1, according to the rules of the procedure.