Question 13.52

22. Suppose that Bob, Carol, and Ted view a cake as having 18 units of value, with each unit of value represented by a small square (as in the accompanying illustration). Suppose, however, that the players value various parts of the cake differently (or that Bob views the cake as being perfectly rectangular, whereas Carol and Ted see it as skewed in opposite ways). We represent this pictorially as follows:

image

Assume that all cuts that will be made are vertical.

  1. If Bob and Carol use divide-and-choose to divide the cake between them, how large a piece will each receive (assuming they follow the suggested strategies that go with divide-and-choose and that Bob is the divider)?
  2. If Carol and Ted use divide-and-choose to divide the cake between them, how large a piece will each receive (assuming that they follow the suggested strategies that go with divide-and-choose and that Carol is the divider)?