Math 103, Section 11, Tuesday, February 22, 2011
Chapter 3 Handout
The Mathematics of Sharing
Assignment Chapter 3A
Please do Exercises 12,18,30, and 32.
Homework will be submitted to Sakai.
Homework to be discussed in class on Friday February 25.
Exercise 7,9, and 11
This is an adorable divider-chooser video on youtube!
Please watch it.
3.1 Fair-Division Games: The Mathematics of Sharing
Basic elements of a fair-division game:
1. The goods or booty
cake, pizza, jewelry, art, land, water rights, drilling rights,
Examples: individuals, clubs, political parties, states, nations
The value systems
Examples: Each player can look at the set S or any part of the set S and
assign to it a value. Either in absolute terms (to me, that’s worth $3.00)
or in relative terms (to me, that piece is worth 25% of the total value of
1. Rationality-each player wants to maximize his or her share of the booty
S. Player uses reason and no psychology, mind games, etc.
2. Cooperation. Players accept the rules of the game. No judges or
3. Privacy. Players have no useful information on the other players’ value
systems and thus of what kinds of moves they are going to make in the