MATH2911/AS2/NTW/ml/09-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2911: Game Theory and Strategy
Assignment 2
Due date: 19/10/2009 before 5:00pm.
1. We shall use the notations given in Denition 2.22. Let p = (p1 , p2 , , pn )
be a mixed
MATH2911
Game Theory and Strategy
27-10-2009 (Examples of Cooperative Games)
Chapter 3 of Robert J. Aumanns Lecture on Game Theory
Chapter 3 of Ein-Ya Gura and Michael B. Maschlers
Insights into Game Theory
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1
In this and subsequent ch
MATH2911
Game Theory and Strategy
27-10-2009
Chapter 3 of Robert J. Aumanns Lecture on Game Theory
Chapter 3 of Ein-Ya Gura and Michael B. Maschlers
Insights into Game Theory
Typeset by FoilTEX
1
Chapter 3: Cooperative Games: Shapley Value
For a coopera
MATH2911
Game Theory and Strategy
29-10-2009
Chapter 3 of Robert J. Aumanns Lecture on Game Theory
Chapter 3 of Ein-Ya Gura and Michael B. Maschlers
Insights into Game Theory
Typeset by FoilTEX
1
Let us reformulate Shapleys conditions concisely:
Symmetr
MATH2911
Game Theory and Strategy
3-11-2009
Chapter 3 of Robert J. Aumanns Lecture on Game Theory
Chapter 3 of Ein-Ya Gura and Michael B. Maschlers
Insights into Game Theory
Typeset by FoilTEX
1
Theorem 3.18 (Shapley [1953]): The Shapley value on N , is
MATH2911
Game Theory and Strategy
10-11-2009
Chapter 4 of Robert J. Aumanns Lecture on Game Theory
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1
Chapter 4: Cooperative Games: The Core
We have seen that the Shapley value of a game gives us a fair way to
measure the contribution
MATH2911
Game Theory and Strategy
17-11-2009
Chapter 5 of Robert J. Aumanns Lecture on Game Theory
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1
Chapter 5: Market Games
We shall apply the Bondareva-Shapley theorem to study the so-called
market game.
In a market game, there is o
MATH2911
Game Theory and Strategy
19-11-2009
Chapter 6 of Robert J. Aumanns Lecture on Game Theory
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1
Chapter 6: The von Neumann-Morgenstern Solution
The von Neumann-Morgenstern solution was the rst solution concept
to be studied (see
MATH2911
Game Theory and Strategy
24-11-2009
Chapter 6 of Robert J. Aumanns Lecture on Game Theory
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1
Chapter 6: The von Neumann-Morgenstern Solution
To prove Proposition 6.6, we shall introduce the following notation
which allows the
Revision on solution concepts
Note that we mainly consider the payo vectors x = (x1, ., xn) Rn,
with xi being the payo to be given to player i N , under the condition
that cooperation in the grand coalition N is reached.
Clearly, the actual formation of t
MATH2911/Test1/TWN/ml/09-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2911: Game Theory and Strategy
Test 1
Date: October 22, 2009
Time allowed: 50 minutes
1. (10 marks)
(a) State the weak form of Zermelos Theorem.
(b) Consider the followi
MATH2911/Test2/TWN/ml/09-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2911: Game Theory and Strategy
Date: November 26, 2009
Time allowed: 50 minutes
1. (10 marks)
A population of birds is distributed so that in any given area there are on
MATH2911
Game Theory and Strategy
20-10-2009
Chapter 2: Application to Evolutionary Biology
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1
Evolutionarily Stable Strategies (ESS)
Recall that a mixed strategy is an ESS if there exists a such that for
every 0 < < and every = , ( ,
MATH2911
Game Theory and Strategy
8-10-2009
Chapter 2: Application to Evolutionary Biology
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1
Evolutionary Game Theory
In two-person games, Nash equilibrium is based on the idea that each
player uses a strategy that is a best response
Game Theory and Strategy
Solutions to Assignment 2
Question 1
Let us start by setting up some notations and doing some remarks. Let
p = (p1 , p2 , , pn ) iN P i be a mixed strategy prole for an n-player
game. And let pi = (pi , pi , , pi i ) be the probab
MATH2911/AS3/NTW/ml/09-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2911: Game Theory and Strategy
Assignment 3
Due date: 16/11/2009 before 5:00pm.
1. Consider a sex ratio game in which females can choose between two pure strategies:
s1 :
Game Theory and Strategy
Solutions to Assignment 3
Question 1
(a) Each female mates only once and produces n osprings. But each male
gets (1 )/ mating, and produces n osprings per mating. Hence the
expected number of grandchildren of a female using strate
MATH2911/AS3/NTW/ml/2009-10
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2911: Game Theory and Strategy
Assignment 4
Due date: 4/12/2009 before 5:00pm
Suggested solution will be posted on 7/12/2009.
1. For the game v (1) = v (2) = v (3) = 0,
Game Theory and Strategy
Solutions to Assignment 4
Question 1
An imputation x = (x1 , x2 , x3 ) is in the core of this game if and only if
x1 + x2 + x3 = 6
x1 + x2
5
x1 + x3
2
x2 + x3
3
x 1 , x2 , x3
0.
From this we get x1
imputation triangle.
3, x2
4, x
MATH2911
Game Theory and Strategy
1-9-2009
Lecturer: Dr. Tuen Wai Ng
Tutor : Mr. Victor Mouquin
Department of Mathematics, HKU
Main goals of this course
An introduction to game theory from a
mathematical perspective.
Provide a good foundation for further
MATH2911
Game Theory and Strategy
8-9-2009
Lecturer: Dr. Tuen Wai Ng
Tutor : Mr. Victor Mouquin
Department of Mathematics, HKU
Definition of Combinatorial Game:
1) There are two players and they move
alternatively.
2) It is deterministic, i.e. there is no
MATH2911
Game Theory and Strategy
22-9-2009
Chapter 2 of Robert J. Aumanns Lecture on Game Theory
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1
Chapter 2: Noncooperative Games
In the Matching Pennies game, there are 2 players whose interests are
completely opposed. It is clear
MATH2911
Game Theory and Strategy
24-9-2009
Chapter 2 of Robert J. Aumanns Lecture on Game Theory
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1
We introduce now the concept of the mixed extension of a game.
Example 2.13: Consider again the game matching pennies. The
interpretat
MATH2911
Game Theory and Strategy
6-10-2009
Chapter 2 of Robert J. Aumanns Lecture on Game Theory
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1
John F. Nash who was awarded the Nobel Prize in Economics for his
seminal works in game theory, proved a general result for the existe
Journal of Peace Research
http:/jpr.sagepub.com/ A Game-Theoretic Interpretation of Sun Tzu's : The Art of War
Emerson M. S. Niou and Peter C. Ordeshook Journal of Peace Research 1994 31: 161 DOI: 10.1177/0022343394031002004 The online version of this art