CO 456 Assignment 1 Fall 2014
Solutions
Problem 1: Bite!
Consider the following impartial game: two players face an m n, rectangular board. A move in this
game is to choose a square and to remove it and all squares to the right and above of it; the bottom

CO 456 Assignment 4 Fall 2014
Solutions
Problem 1:
Find all the mixed strategy Nash equilibria in the following two games:
6, 0
3, 2
0, 6
6, 0
0, 1
2, 2
0, 2
0, 1
Solution: Consider the left game rst. Let (, 1 ) and (, 1 ) be the mixed strategies of the t

CO 456 Practice Final Exam, Fall 2014
UNIVERSITY OF WATERLOO
CO456 PRACTICE FINAL EXAMINATION
FALL TERM 2014
Page 1
CO 456 Practice Final Exam, Fall 2014
Page 2
Problem 1: Pure Equilibria
A famous tradition in bullghting matches is that a victorious bullg

Surname:(Print)
First Name:
Signature:
Id.#:
University of Waterloo
CO459 Introduction to Game Theory
Midterm Test
October 25, 2005
7:00 9:00 p.m.
INSTRUCTIONS:
1. Write your name, Id.#, and signature in the blanks above.
2. There are 11 pages in this exa

CO 456 Assignment 5 Fall 2014
Solutions
Problem 1: Mixed Equilibria
Consider the 2-player with the following payo matrix:
L
1,2
2,1
1,2
T
M
B
C
3,1
4,0
1,3
R
1,4
0,2
2,0
Is the mixed strategy-prole given by x1 = (0, 2/3, 1/3), x2 = (2/3, 0, 1/3) a Nash eq

CO 456 Assignment 3 Fall 2014
Solutions
Problem 1: Best responses
Two players in the game of Two-Finger Morra simultaneously put out either one or two ngers. Each
player must also announce the number of ngers that he believes his opponent has put out. If

CO 456 Assignment 2 Fall 2014
Solutions
Problem 1: Dominos . again!
Recall the rules of the Dominos game from question 2 of assignment 1, and consider playing it on a 1 n
board for n N. Let Dn be the NIM value of this game so that the starting position of

C O456 I NTRODUCTION TO G AME T HEORY - M IDTERM S OLUTIONS
Problem 1.
(1) If all vi are some common value v , then the action prole a with ai = v for all 1 i n is
an equilibrium because all players are earning utility 0, which cannot be improved by switc

CO 456: Assignment 1
Due Wed, September 26 in class.
Include your name and ID number.
Write the number of pages on the front page and number each page.
Problem 1 - 5 marks
If k = n k , then the only PNE is when all citizens vote. To see that this is a PNE

CO 456: Assignment 5 Solutions
Problem 1
1. Let a denote the assignment we are going to build. Initially, N0 is the set of all players. The cycles in
G[N0 ] are 1 7 1 and the loop 2 2. So, we set a(1) = 7, a(7) = 1 and a(2) = 2.
Now N1 = cfw_3, 4, 5, 6, 8

CO 456: Assignment 4 Solutions
Problem 1
1. Suppose player i changes their path Pi to Pi to strictly lower their penalty. Every edge e Pi Pi
contributes the same to both ui (f ) and ui (Pi , fi ). Every e Pi Pi contributes ri ce (fe ) to ui (f ),
but none

CO 456: Assignment 2
Due Wed, October 10 in class.
Include your name and ID number.
Write the number of pages on the front page and number each page.
Problem 1 - 5 Marks
Consider the following 2-player strategic game.
The best responses have been highlig

CO 456: Assignment 6 Solutions
Problem 1 - 6 Marks
The matching that maximizes the total value has m(1) = a, m(2) = unassigned, m(3) = c, and m(4) = b.
The total social welfare of this matching is 25.
The payments and utilities are calculated as follows.

CO 456: Assignment 3
Due Wed, October 24 in class.
Include your name and ID number.
Write the number of pages on the front page and number each page.
Throughout the entire assignment, the price of anarchy/stability will be with respect to pure strategies