NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264 Game Theory
Tutorial 2
1. Consider two animals that fight over valuable territory. There are two possible pure
strategies for each. The hawk (H) strategy is to escalate battl

Part 2: Dynamic Games of Complete Information
By complete information, we mean that the
payoff functions are common knowledge. We will
consider 2 cases:
(1) Dynamic games with complete and perfect information
By perfect information, we mean that at each
m

Part 3: Static Games of Incomplete Information
Games of incomplete information are also called
Bayesian games.
In a game of incomplete information, at least one
player is uncertain about another players payoff function.
Cournot competition under asymmetri

4.3
Job-Market Signaling
In the model of job-market signaling, the sender is
a worker, the receiver is the market of prospective
employers, the type is the workers productive ability, the message is the workers education choice,
and the action is the wage

Sequential Bargaining
Players 1 and 2 are bargaining over one dollar. They
discount payoffs received a period later by a factor
with 0 < < 1.
The three-period bargaining game:
(1a) In the first period, player 1 proposes s1(1) for
himself and s2(1) for pl

Example. The worker has an outside opportunity v known by himself. The firm believes that
v = 6 and v = 10 with probabilities 2/3 and 1/3
respectively. A wage w = 8 is preset by the union.
The firm and the worker simultaneously announce
whether to accept

Example 6:
(1) Player 1 chooses an action a1 from A1 = cfw_L, R.
(2) Player 2 observes a1 and then chooses an action
a2 from A2 = cfw_L0, R0.
(3) Player 3 observe whether or not (a1, a2) = (R, R0)
and then chooses an action a3 from A3 = cfw_L00, R00.
1
2"

NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264
Assignment 1-Answers
1. Three individuals, A, B and C, are playing a simultaneous move game.
Each has two strategies, Grab and Do not grab. The payoffs are
as follows. If all

Game Theory
MA4264
Aims and Objectives: Game theory provides
a mathematical tool for multi-person decision making. This module is an introduction to game theory, studying basic concepts, models and solutions
of games and their applications.
Topics: Games

Find mixed-strategy Nash equilibria
We only consider two-player games in which each
player has 2 pure strategies, so that we can use the
graphical approach.
Let p1 = (r, 1 r) be a mixed strategy for player
1 and p2 = (q, 1 q) a mixed strategy for player 2

MA4264 GAME THEORY
SEMESTER 2, 2015-2016
Prerequisite
:
(MA3236 or MA3252) and (MA2216 or ST2131 or ST2334)
Preclusion
:
EC3312
Modular Credit
:
4 Modular Credits
Lecturer
Name:
Email:
Telephone:
Office:
SUN Yeneng
ynsun@nus.edu.sg
6516 3344
S17, #05-02
S

NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264 Game Theory
Tutorial 3
1. Find the mixed-strategy Nash equilibrium of the following normal-form games.
T
B
L
2, 1
1, 2
R
0, 2
3, 0
L
C
R
T
2,0
1,1
4,2
M
3,4
1,2
2,3
B
1,3
0,2

5
Part 5: Cooperative Games
In cooperative games binding agreements may be made
among the players. In addition, we assume that all
payoffs are measured in the same units and that there
is a transferrable utility which allows side payments
to be made among

NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264
Assignment 2
Please write down your tutorial group number and submit the solutions
to your tutor in class or to the envelop next to his/her office door
by 10 pm, Wednesday, 6

NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264 Game Theory
Tutorial 1
1. In the following normal-form game, what strategies survive iterated elimination of
strictly dominated strategies? What are the pure-strategy Nash eq

NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
2015/2016 (II)
MA4264
Assignment 1
Please write down your tutorial group number and submit the solutions
to your tutor in class or to the envelop next to his/her office door
by 10 pm, Wednesday, 2