The following problems use the last-diminisher method of fair division. Using the last-...

The following problems use the last-diminisher method of fair division.

Using the last-diminisher method, four players will divide a pie. Player 1 cuts a slice of pie that player 1 believes is valued at one-fourth of the entire pie. Each player, in order, either will judge the piece acceptable or will cut it smaller. The results of the first round are in the following table.

a. Which player keeps the piece of pie at the end of the first round?

b. Player 1 begins the second round by cutting a piece of pie. What value will player 1 put on the piece cut?

c. If player 2 and player 4 then both trim the piece of pie, who will keep the piece?

d. Who are the final two players, and how will they divide the rest of the pie equitably?