Chapter 3, Problem 59E

Ana, Belle, and Chloe are dividing 3 Choko bars, 3 Minto bars, and 3 Frooto bars among themselves using the method of markers. The players’ value systems are as follows: $\left(1\right)$ Ana likes Choko, Minto, and Frooto bars the same; $\left(2\right)$ Belle loves Minto bars but hates Choko and Frooto bars; $\left(3\right)$ Chloe likes Frooto bars twice as much as she likes Choko or Minto bars. Suppose that the candy is lined up exactly as shown in Fig. 3-37.

Figure 3-37

a. Describe the placement of each player's markers. (Use A1. and A2 for Ana's markers, B1 and B2 for Belle's markers, and C1 and C2 for Chloe's markers.)

(Hint: For each player, compute the value of each piece as a fraction of the value of the booty first. This will help you figure out where the players would place their markers.)

b. Describe the allocation of candy to each player and which pieces of candy are left over.

c. Suppose that the players decide to divide the left over pieces by a random lottery in which each player gets to chose one piece. Suppose that Belle gets to choose first, Chloe second, and Ana last. Describe the division of the leftover pieces.