15-896 Algorithms, Games, and Networks
Homework # 1
Solutions
Exercises:
1. Go with your strengths? Recall that in the penalty-shot game the shooter can
shoot left or shoot right, and the goalie can dive left or dive right. If the goalie guesses
correctly
15-896 Algorithms, Games, and Networks
Homework # 3
Solutions
Exercises:
1. VCG interpretation Consider the VCG mechanism with Clarke pivot rule (i.e.,
charge each player their externality) for the case of k identical printers. Assume each
player i has va
15896 Homework #4: Fair Division and Kidney Exchange
Solution
Ariel Procaccia
1
Problem 1
(a) Let ti , . . . , ti be points such that Vi is uniformly distributed on each [ti , ti +1 ]. Make a mark
ss
1
K
at each of these points and let J denote the subi
15896 Homework #2: Social Choice
Solution
Ariel Procaccia
1
Problem 1
(a) Consider the following preference prole.
6 voters
c
a
b
2 voters
b
a
c
3 voters
b
c
a
4 voters
a
b
c
2 voters
a
c
b
Alternative c is the winner, but when the rightmost group of tw