Fair Division Games

Which of the following items are discrete items? Choose all that apply.

• pizza

• house

• watch

• children

• cake

Which of the following items are continuous items? Choose all that apply.

• land

• money

• diamond ring

• dog

• pecan pie

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Alice? Choose all that apply.

• S₁

• S₂

• S₃

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Bob? Choose all that apply.

• S₁

• S₂

• S₃

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which of the shares are fair shares to Carlos? Choose all that apply.

• S₁

• S₂

• S₃

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Find all possible fair divisions for this problem.

• Alice gets S₁, Bob gets S₃, Carlos gets S₂

• Alice gets S₃, Bob gets S₁, Carlos gets S₂

• Alice gets S₁, Bob gets S₂, Carlos gets S₃

• Alice gets S₃, Bob gets S₂, Carlos gets S₁

Alice, Bob and Carlos are dividing among themselves the family farm. The property is divided into three shares and the table above shows the values of the shares to each player.

Which fair division is the best?

• Alice gets S₁, Bob gets S₃, Carlos gets S₂

• Alice gets S₃, Bob gets S₁, Carlos gets S₂

• Alice gets S₁, Bob gets S₂, Carlos gets S₃

• Alice gets S₃, Bob gets S₂, Carlos gets S₁

Blanche, Dorothy, Rose and Sophia are dividing a cheesecake that had previously been divided into four slices.

Since there are four players in this problem, what is the minimum value of a fair share? Please give your answer in the form of a percent.

Blanche, Dorothy, Rose and Sophia are dividing a cheesecake that had previously been divided into four slices. The table above shows the values of the slices in the eyes of each player.

Which of the slices are fair shares to Blanche? Choose all that apply.

• S₁

• S₂

• S₃

• S₄

Blanche, Dorothy, Rose and Sophia are dividing a cheesecake that had previously been divided into four slices. The table above shows the values of the slices in the eyes of each player.

Which of the slices are fair shares to Dorothy? Choose all that apply.

• S₁

• S₂

• S₃

• S₄