MA 103 Chapter Notes - Chapter 3-4: Fair Division, Hamilton, Mississippi, Themarker
Document Summary
Vocabulary: fair division: dividing an object or collection of objects fairly fair share: if we have n players, fair share is 1/n of the total value. Assumptions about players: everybody acts rationally, based on logic and not emotions, players know nothing about each other"s value systems, value systems: what"s important to that particular person. Types of problems: continuous: one thing is being split up, discrete: multiple objects must be divided. You like strawberry (s) 3x as much as chocolate (c). If s = 3 and c = 1, the total value of this cake is 4. If the cake costs , then the strawberry half is worth () and the chocolate half is worth () to you. You like vanilla twice as much as chocolate, and chocolate three times as much as strawberry. Thus, s = 1, v = 2c, and c = 3s; s = 1, v = 6, and c = 3.
