2
1. Find the N ash bargaining model NTU solution to the bimatrix game
[E313 8:3]
with threat point (3 1).
3:31;) LL1-3>( WWW/Wu)
_ jaw/Ww'W/z
I ' ' , 5m +14 : O U 3 H75
f 3
2. Given the bimatrix game below, nd all real numbers 3 and t such that the ga
Math 167, Winter 2016, UCLA
Name:
Instructor: Steven Heilman
UCLA ID:
Date:
Signature:
.
(By signing here, I certify that I have taken this test while refraining from cheating.)
Mid-Term 1
This exam contains 7 pages (including this cover page) and 5 probl
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due March 8th, in the discussion section.
Homework 8
Exercise 1. Prove the following Lemma from the notes: The set of functions cfw_WS Scfw_1,.,n
is
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due March 1st, in the discussion section.
Homework 7
Exercise 1. Let n be a positive integer. Let v : 2cfw_1,.,n cfw_0, 1 be a characteristic functio
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due February 23rd, in the discussion section.
Homework 6
Player I
Exercise 1. Recall the Game of Chicken is defined as follows. Each player chooses t
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due February 16th, in the discussion section.
Homework 5
Exercise 1. Suppose we have a two-person zero-sum game with (n + 1) (n + 1) payoff
matrix A
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due February 9th, in the discussion section.
Homework 4
Exercise 1. Find the value of the two-person zero-sum game described by the payoff matrix
0 9
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due February 2nd, in the discussion section.
Homework 3
Exercise 1. This exercise deals with subsets of the real line. Show that [0, 1] is closed, bu
Game Theory
Steven Heilman
Please provide complete and well-written solutions to the following exercises.
Due April 5, in the discussion section.
Homework 1
Exercise 1. Let n be a positive integer. Consider the game Chomp played on an n n
board. Explicitl
Solutions to Homework 3 Exercises from Part I I of Fergusons Game Theory
Section 1.5
1.5#2 Player I holds a black Ace and a red 8. Player II holds a red 2 and a black 7. If the chosen cards
are of the same color Player I wins, if they differ Player II doe
Solutions to Exercises from Part I of Fergusons Game Theory
Section 1.5
1.5#1 Mis`ere version of the take-away game. There are 21 chips, we can remove 1, 2, or 3.
Last player to move loses, hence position 1 is a P-position, from positions 2,3, and 4 we ca
Solutions to Exercises from HW5, Math 432, Spring 2012
Section 1.6
1.6#2 Find the safety levels and maxmin strategies for the players in the bimatrix games
(a)
A=
B =
(5, 0)
(4, 4)
5
, saddle point: VI = 1, p = (1, 0).
4
1
0
T
(1, 1)
(0, 5)
5
, saddle poi
Solutions to Homework 2 Exercises from Part I of Fergusons Game Theory
4.5#4 Kayles problem of Dudeney and Loyd
Of 13 pins in a row the second has been knocked down.
(a) In order to show that this is an N-position, we have to prove that the SG value at th
Solutions to Exercises from Homework 4, Math 432 Spring 2012
4.7#1 Consider the game with matrix
0
A = 1
9
7
4
3
2
8
1
4
2 .
6
(a) A Bayes strategy against (1/5, 1/5, 1/5, 2/5) is the row which gives the best payoff for Player I.
Row 1 gives 7/5 + 2/5 + 8
167 Midterm 1 Solutions1
1. Question 1
(i) Give an example of a game mentioned in class, or the notes, or any course textbook,
such that: the first player has a winning strategy. (You only need to mention the game; you
do not need to prove anything.)
Solu