Question 13.59
29. Suppose Players 1, 2, and 3 view the cake as in Exercise 25. Illustrate the envy-free procedure for (yielding an allocation of part of the cake) by following steps (a) through (c) below. Again, restrict attention to vertical cuts.
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- 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 , , and . (This is the same as Exercise 25a.)
- Redraw the picture from Player 2’s view, and illustrate the trimming of piece that he or she would do. Label the trimmed piece and the actual trimmings .
- Indicate which piece each player would choose (and what he or she thinks its size is) if the players choose in the following order, according to the envy-free procedure: Player 3, Player 2, Player 1.
29.
(a) See figures below.
(b) See figures below.
(c) Player 3 will choose (which he thinks is of size 6 square units). Player 2 will choose (which he thinks is of size 5 square units). Player 1 will receive (which he thinks is of size 6 square units). The proviso does not come into play (since Player 3 took the trimmed piece).