CHAPTER 7
Simultaneous-Move Games with Mixed Strategies I:
Zero-Sum Games
Teaching suggestions
This chapter introduces mixed strategies and the methods used to solve for mixed
strategy equilibria in zero-sum games. Students are likely to accept the idea o

CHAPTER 4
Simultaneous-Move Games with Pure Strategies I:
Discrete Strategies
Teaching suggestions
This chapter develops a succession of examples to illustrate the concept of Nash
equilibrium when each player chooses from a finite number of discrete pure

CHAPTER 12
Collective-Action Games
Teaching suggestions
A good way to introduce the topic of coordination games is to have the students play one.
There are two suggestions below. One can be used to lead into a general discussion of the issues
surrounding

CHAPTER 5
Simultaneous-Move Games with Pure Strategies II:
Continuous Strategies and III: Discussion and Evidence
Teaching suggestions
The basic concepts of simultaneous moves, best responses, and Nash equilibrium were
motivated in Chapter 4 in the contex

PART TWOConcepts and Techniques
CHAPTER 3
Games with Sequential Moves
Teaching suggestions
Most students find the idea of rollback very simple and natural, even without drawing or
understanding trees. Of course, they start by being able to do only one or

CHAPTER 6
Combining Sequential and Simultaneous Moves
Teaching suggestions
This chapter introduces three new concepts and associated techniques: (1) multistage games where
a simultaneous-move game occurs at one or more of the stages, (2) the effects of ch

CHAPTER 8
Simultaneous-Move Games with Mixed Strategies II:
Some General Theory
Teaching suggestions
Getting students to accept and to understand the idea of mixing in non-zero-sum games is
even harder than in zero-sum games. In zero-sum games, if one pla

CHAPTER 13
Evolutionary Games
Teaching suggestions
How much time you want to spend on this material will depend on the focus of your
course. For many social science courses, a general exposure to the ideas, based on a quick run
through the special example

Evolutionary Games
Game theory, like economics, employs a strong assumption: rationality.
Well explore the consequences of dropping rationality in game theory. (I
believe that dropping rationality altogether is a stronger assumption than
imposing rational

Collective Actions
Public good is a typical example of collective action problems. A large
number of people, N , are involved. Each person can choose to participate
and contribute or to shirk. If the number of participants is n, the (nonexcludable) public

Sequential-Simultaneous Games
Subgame perfect equilibrium is used to solve sequential games and Nash
equilibrium simultaneous games. How are we going to solve games with both
simultaneous and sequential moves?
Dont
GLOBALDIALOG
Invest
High
Dont
0, 0
14
0,

Prisoners Dilemma and Repeated Games
In a one-shot prisoners dilemma (Figure 10.2), the dominant strategy is
to defect. However, the two players can mutually benefit from cooperating.
Will the two players cooperate if the game is repeated?
XAVIERS TAPAS
2

Simultaneous Games - Pure Strategies I
Dominant Strategy
The police have sufficient evidence to send a husband and wife to jail
three years for kidnapping. They need at least one of them to confess in
order to send the other a much longer sentence (25 yea

Uncertainty and Information
Signaling and Screening
In general, signals are costly and the costs vary across different types of
individuals. It is then more likely for individuals with a lower cost to send a
signal. Hence, the signal can be used to infer

Simultaneous Games - Mixed Strategies I
Expected Utility Hypothesis
How do people evaluate a gamble?
Figures 8A.1-8A.2
Matching Pennies Revisited
KID 1
H
T
KID 2
H
T
1, 1 1, 1
1, 1 1, 1
What is the Nash equilibrium of this game?
How will you play the game

Sequential Games
Tian Ji Horse Race
It is a story in the Warring States Period. King Wei of Qi enjoyed racing horses with General Tian Ji. The horses of King Wei were better than
General Tians. King Wei always won. There were usually three matches:
Kings

Simultaneous Games - Mixed Strategies II
Mixed-Strategy Nash Equilibrium
KICKER
Left (pL )
Center
Right (pR )
GOALIE
Left (qL ) Center Right (qR )
45
90
90
85
0
85
95
95
60
Figure 7.10 Penalty Kick
Does the game have a Nash equilibrium in pure strategies?

ECON0106/2214 Games and Decisions
Tutorial 4 Rationalizability, Mixed Strategies
Q1.
COLUMN
Row
Earth
Water
Wind
Fire
North
1,3
1,2
3,2
2,0
South
3,1
1,2
2,1
3,0
East
0,2
2,3
1,3
1,1
West
1,1
1,1
0,3
2,2
What are the rationalizable strategies for each pla

a)
6, 6
4, 7
7, 4
5, 5
4, 7
2, 8
5, 5
3, 6
7, 4
5, 5
8, 2
6, 3
5, 5
3, 6
6, 3
4, 4
The subgame-perfect equilibrium of this game is (DDDDD, DDDDD). So you and your
friend will not cooperate with each other, i.e. will not contribute any effort in the two
pr

Q1)
Water and Fire for Row and East and West for Column are rationalizable.
Q2)
3 PSNE: (P, P), (S, S) and (B, B)
TheequilibriumwhenHarryandSallybothmixoveronlyPastaandSandwichis:
Harryplays5/6(Pasta)+1/6(Sandwich)
Sallyplays1/6(Pasta)+5/6(Sandwich)
Theeq

1
No pure strategies NE.
4
Your
expected payof
3
2
1
0
P= 1
P= 0
0
1
-1
-2
q
1
X
X
X
X X XX XX X X X X X X XX
X
X
X
X
X
X
X
p
0
1
X BR of you
BR of your friend
5
4
3
q= 1
q= 0
2
1
0
0
1
q
X
1
X
X
X X X XX X X X X X X X X X
X
X
X
X
X
X
X
p
0
X BR of you

ECON0106/2214 Games and Decisions
Tutorial 3 - Simultaneous Games
Q1.
Consider a game in which there is a prize worth $30. There are three contestants,
Larry, Curly, and Moe. Each can buy a ticket worth $15 or $30 or not buy a ticket at
all. They make the

Q1
Kid 2 has 9 strategies.
They are:aa, ab, ac, ba, bb, bc, ca, cb, cc
There are 3 unconditional strategies: aa, bb, cc.
And 6 conditional strategies: ab, ac ,ba, bc, ca, cb.
There are 2 subgame perfect equilibrium:
(N, aa), (S, aa)
Simultaneous Games:
Ga

ECON0106/2214 Games and Decisions
Tutorial 1 Answer
1)
Kid 13 strategies: N, E, S
Kid 28 strategies: aaa, aab, aba, abb, baa, bab, bba, bbb
The equilibrium strategies are N for Kid 1 and bab for Kid 2. The payoff is (2,1). The
equilibrium path is Kid 1 ch

ECON0106/2214 Games and Decisions
Tutorial 5 Mixed Strategies, Sequential-Simultaneous Games
Q1.
You are planning to have lunch after class. You prefer to have lunch with your friend
but cannot find him by phone. Yet, your friend does not want to meet you

ECON0106/2214 Games and Decisions
Tutorial 6 Repeated Games
Q1.
You and your friend are forming a group for the group project in an economics
course. Both of you prefer contributing less effort on the project. However, if you two
dont making any contribut

ECON0106/2214 Games and Decisions
Tutorial 2 - Sequential Games, Simultaneous Games
Q1.
a
Kid 2
N
b
3, 2
2, 0
c
3, 0
a
3, 4
Kid 1
S
Kid 2
b
c
1, 2
1, 0
a) Count and list all the strategies of Kid 2. How many conditional strategies?
b) Find out the subgame

ECON0106/2214 Games and Decisions
Tutorial 1 - Sequential Games
Q1. In each of the following games:
a) Count and list all the pure strategies for each player
b) Find out the equilibrium path and subgame perfect equilibrium.
i)
Kid 2
b
N
Kid 1
a
Kid 2
E
S