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
strategi
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 env
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, G
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EQUILIBRIUM POINTS IN Air-PERSON GAMES
BY JOHN F. NASH, JR?
PRINCETON UNIVERSITY
Communicated by S. Ischetz, November 16, 19-19
One may dene a concept of an n-person game in which each player has
a fi
Solution to Tutorial 2
2015/2016 Semester II
MA4264
Game Theory
January 28, 2016
Exercise 1.
Solution. (a) vw
2 < 0 or v < w. (b) Note that v >
the condition is vw
2 > 0 or v > w.
v
2
t since v > 0 a
A Past Final Exam
1. (10 marks) Suppose that a seller wants to sell his used car. The seller knows the
quality of the car, but the buyer does not. The buyer knows only that the car could
be a good qua
Solution to Tutorial 3
2015/2016 Semester II
1
MA4264
Game Theory
Tutorial
Exercise 1.
Solution. [A Useful Claim: Let be a Nash equilibrium. Then, for every player i, every
pure strategy in the suppor
Solution to Mid-term Test
2015/2016 Semester II
MA4264
Game Theory
Question 1.
Solution. (a) Strategy C is strictly dominated by R. After the elimination of C, M is
strictly dominated by U . Hence, bo
Solution to Tutorial 4
2015/2016 Semester II
1
MA4264
Game Theory
Tutorial
Exercise 1.
Solution and Proof.
(Ultimatum with a Finite Number of Alternatives) (a) game tree
1d
"b
b
"
b
"
b
"
b 10
"
0"
1
6
6.1
Additional Examples
The Market for Lemons
Suppose a seller wants to sell his used car. The seller
knows what the quality of the car is, but the buyer
does not. The buyer knows only that the car
Solution to Tutorial 1
2015/2016 Semester II
1
MA4264
Game Theory
Tutorial 1
Exercise 1. In the following normal-form games, what strategies survive iterated elimination of strictly dominated strategi
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 inf
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 env
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 transferra
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
A game with 3 players
Player 3
A3
Player 1 A A
1, 0, 2
1 2
&
A1B2
5, 2, 3
Player 2 B A
0, 2, 1
1 2
B1B2
2, 3, 3
B3
3, 5, 1
2, 1, 5
2, 2, 5
1, 4, 0
This game can also be represented as
A3
B3
A2
1, 0, 2
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 p
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 so
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
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 an
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 perio
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 t
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 playe
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 d