Monty and Albert place a divider in their shared bedroom. Monty thinks that div...

Monty and Albert place a divider in their shared bedroom.

Monty thinks that dividing the room in half is fair, and he does not care which half he gets. Albert would prefer a window on his half of the room. Using the divide-and-choose method for two players, consider three possible divisions Monty could make in the room.

a. Visually inspect the two halves in (I), and explain which half Albert would select and why. You need not assign numerical values to the pieces.

b. Visually inspect the two halves in (II), explain which half Albert would select and why. You need not assign numerical values to the pieces.

c. Visually inspect the two halves in (III), explain which half Albert would select and why. You need not assign numerical values to the pieces.

d. Suppose in division (I), Albert selects the left half, leaving the right half for Monty. How would each judge the fairness of the portion they received compared to the value of the entire room?