Fair Division

Three players (Ady, Brenden, and Cara) are sharing a pie. Suppose that the pie is divided into three slices (S1 ,S2 , and S3 ). The following table gives the value of each slice in the eyes of each of the players.

Which of the three slices are fair shares to Ady?

Angela and Ben want to divide fairly the chocolate-strawberry cake shown below. The total cost of the cake was $6.00. Angela values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values strawberry.

In Angela's eyes, the piece shown below is worth?

Angela and Ben want to divide fairly the chocolate-strawberry cake shown below. The total cost of the cake was $6.00. Angela values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values strawberry.

In Ben's eyes, the piece shown below is worth?

Ned buys a chocolate-strawberry-vanilla cake in Figure (i) for $14.00. He cuts the cake into six 60° wedges as shown in Figure (ii). Ned values strawberry six times as much as chocolate. He does not value vanilla cake at all.

How much does Ned value piece 4?

Ned buys a chocolate-strawberry-vanilla cake in Figure (i) for $14.00. He cuts the cake into six 60° wedges as shown in Figure (ii). Ned values strawberry six times as much as chocolate. He does not value vanilla cake at all.

How much does Ned value piece 3?

Brenda and Eddy buy a 12-in half ham, half turkey sub sandwich for $4.80. Eddy values ham 3 three as much as turkey.

What is the value of 1-inch of turkey to Eddy?

Brenda and Eddy buy a 12-in half ham, half turkey sub sandwich for $4.80. Eddy values ham 3 three as much as turkey.

What is the value of 1 inch of ham to Eddy?

Four heirs must divide an estate consisting of a house and a cabin. Use the table to determine how much is a fair share to Player A?

Four heirs must divide an estate consisting of a house and a cabin. In the initial allocation, what did player B receive?

Four investors purchase a piece of land for one million dollars and decided to divide it fairly among themselves using the last diminisher method. The investors are Aaron, Betty, Carla, and David in that order. In round 1, the only diminisher is Carla. In round 2, Betty is the only diminisher, and there are no diminishers in round 3. List the order in which the players received their pieces.