Question 13.54
24. Suppose that Players 1, 2, and 3 view a cake as in Exercise 22. Notice that each player views the cake as having 18 square units of area (or value). Assume that each player regards a piece as acceptable if and only if it is at least square units of area (his or her “fair share”). Assume also that all cuts made correspond to vertical lines.
- Provide 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 .
- Identify two of these pieces that Player 2 finds acceptable and two that Player 3 finds acceptable.
- Show that a feasible assignment of fair pieces can be achieved by letting the players choose in the following order: Player 3, Player 2, Player 1. Indicate how many square units of value each player thinks he or she received. Is there any other order in which players can choose pieces (in this example) that also results in a feasible assignment?