Welcome to
EC 209: Managerial
Economics- Group A
By: Dr. Jacqueline Khorassani
Week Eleven
1
Managerial EconomicsGroup A
Week Eleven- Class 1
Monday, November 12
11:10-12:00
Fottrell (AM)
Aplia assignment is due
tomorrow before 5 PM
2
I received Questions
1.
2.
3.
What is the format of the exam?
If you are leaving Dec. 1 who will be
grading our exams?
There are aplia assignments online
through mid December, well after classes
are over. How many more aplia
assignments are there?
Thank you.
3
Answers


I will give you the format of the exam
and who will grade it soon.
There are two more aplia assignments
after this week
– A total of 10 assignments
– Only the top 8 count
4
Question

in this weeks aplia assignment, Q7, we have to get
the reaction function of 2 microbreweries given
their demand functions. To do this we have to find
MR and set it equal to MC. I have done this and
none of the answers given match the answer i got
even though i have tried it many times following
the matching question in the practice set. I was
wondering if you could check if the right answer is
included in the ones given or not.
Thanks
5
Answer



Please note that the hint in question 7 of
the graded assignment due next Tuesday is
incorrect. The correct hint is as follows:
When a firm's demand has the form Q1 = a
- bP1 + cP2 (where a, b and c are
constants), Firm 1 has marginal revenue of
MR1 = a + cP2 - 2bP1
(Note that the hint on number 7 in the
practice assignment is correct)
6
Managerial Economics &
Business Strategy
Chapter 10
Game Theory: Inside
Oligopoly
7
What is a game?





A situation in which players make strategic
decisions.
A strategy is a plan of action for playing the
game.
A payoff is the value associated with a
possible outcome.
Initially, we will assume rationality on the
part of players.
A key issue is what kind of information is
available to the players.
8
Non-cooperative vs.
Cooperative Games

A cooperative game
– participants can negotiate binding
contracts that allow them to plan joint
strategies
– Example: bargaining over the price of a
car.
9
Non-cooperative vs.
Cooperative Games

Non-Cooperative Games
– Both players have to make decisions
without knowing what the other player is
going to do.
– Example: Prisoner’s Dilemma game.
10
What are Normal Form
Games?



Simultaneous-move games versus
sequential move games
One-shot game versus repeated games
A Normal Form Game consists of:
– Players.
– Strategies or feasible actions.
– Payoffs.
11
What is a dominant
strategy?

A player has a dominant strategy if it
would choose a particular strategy
regardless of what the other player
does.
12
Example 1: Player A can choose Up or Down while
player B can choose Left or Right.
First payoff in each cell is the payoff for Player A.
Who has a dominant
strategy?
A
What should B do?
Left
13
What is Nash
Equilibrium?


A set of strategies such that each
player is doing the best it can given
the strategy of the other players.
(Up, Left) is a Nash equilibrium
14
Example 2
Player 1
Player 2
Strategy
a
b
c
A
B
C
12,11
11,10
10,15
11,12
10,11
10,13
14,13
12,12
13,14
Does anyone have a dominant strategy?
Yes, Player 1 does
15
Example 2


Regardless of whether Player 2 chooses A, B,
or C, Player 1 is better off choosing “a”!
“a” is Player 1’s Dominant Strategy!
Player 1
Player 2
Strategy
a
b
c
A
B
C
12,11
11,10
10,15
11,12
10,11
10,13
14,13
12,12
13,14
16
What should player 2 do?

2 has no dominant strategy!
– But 2 should reason that 1 will play “a”.
– Therefore 2 should choose “C”.
Player 1
Player 2
Strategy
a
b
c
A
B
C
12,11
11,10
10,15
11,12
10,11
10,13
14,13
12,12
13,14
17
The Outcome
Player 1
Player 2

Strategy
a
b
c
A
B
C
12,11
11,10
10,15
11,12
14,13
10,11
10,13
12,12
13,14
This outcome is a Nash equilibrium:
– “a” is player 1’s best response to “C”.
– “C” is player 2’s best response to “a”.
18
Example 3: Simultaneous
moves. One-shot game
Is Nash
Equilibrium
the best
outcome?
No, HighHigh is
Both
have
incentive
to cheat
What would A do?
What would B do?
Nash Equilibrium?
Low Price
Low price
Low Price-Low Price
19
Managerial EconomicsGroup A

Week Eleven- Class 2
– Tuesday, November 13
– Cairnes
– 15:10-16:00

Aplia assignment is due before 5PM today
– Question 7 is deleted
– If you have submitted this assignment already
you should go back to the work you submitted
and delete any answers you submitted on
question 7.
20
The Market-Share Game
in Normal Form
Manager 1
Manager 2
Strategy
P=$10
P=$5
P=$1
P=$10
.5, .5
.8, .2
.9, .1
P=$5
.2, .8
.5, .5
.8, .2
P = $1
.1, .9
.2, .8
.5, .5
Does anyone have a dominant strategy?
Both do
21
Market-Share Game
Equilibrium
Manager 1
Manager 2
Strategy
P=$10
P=$5
P=$1
P=$10
.5, .5
.8, .2
.9, .1
P=$5
.2, .8
.5, .5
.8, .2
P = $1
.1, .9
.2, .8
.5, .5
Nash Equilibrium
22
Example 4 – Advertising
Game
Does
anyone
have a
dominant
strategy?
Both do
What is the Nash Equilibrium?
23
Both advertise
Example 5 – Coordination
game There is an incentive to
cooperate
Who has a dominant strategy?
No one
There are two
Nash equilibria
24
Example 6 – Monitoring employees
What should manger do?
Say she will monitor but actually not do it
Incentive
to hide
strategy
Who has a dominant
strategy?
No one
What is the equilibrium?
No equilibrium
25
Infinitely repeated games
In many situations the players interact with
each other on a regular basis.
 Remember that a euro earned today is worth
more than euros earned in the future.
 Remember from before that If the profit is the
same in each period and the horizon is infinite,
then
PV = π (1+i) /i

– PV is Present Value
– where π is the profit earned in each period,
– i is the discount rate.
26
What is the Nash Equilibrium in
a one shot game?
Both Firms charge low price.
27
What if the Pricing Game is
repeated & the firms agree
to charge a high price ?


A trigger strategy is a strategy that is
contingent on the past plays of the
game.
Trigger strategy:
– If one firm cheats the other will charge
the lower price forever. Let’s examine the
incentives to cheat under this strategy.
28
What If Firm A cheats?
What is the PV of cheating?
Present value of cheating is 50 + 0 + 0 + …. = 50
.
Present value of cooperating is 10 + 10 /(1+i)+ 10 (1+i)2 + … = 10
(1+i)/i.
Cheating is the better option if 50 > 10(1 + i)/i.
This is true when i > 0.25 (25 per cent).
29
Key Insights:



Not all games are games of conflict.
Communication can help solve
coordination problems.
Sequential moves can help solve
coordination problems.
30
Factors affecting collusion in
repeated games





Knowledge of other firms
Knowledge of customers of other firms
Knowledge of when collusive
agreements are broken
Is punishment possible?
Are threats credible?
31
Finitely Repeated Games:
Uncertain final period


Suppose the firms do not know the
exact date at which the game ends.
Suppose the probability that the game
will end after a given play is Φ, where
0 < Φ < 1.
32
Suppose Φ = 0.4, that
means that probability of
not ending the game is 0.6




There is a 0.4 (40%) chance that the game
will end after one play,
There is a 0.6 * 0.4 = 0 .24 (24%) chance
it will end after two plays
There is a 0.6 * 0.6 * 0.4 = 0.144 (14%)
chance it will end after three plays
….Probability of ending the game zero
33
Therefore

A finitely repeated game when there is
uncertainty about the final period
turns out to be exactly the same as an
infinitely repeated game.
34
Managerial EconomicsGroup A

Week Eleven- Class 3
– Thursday, November 15
– 15:10-16:00
– Tyndall

Next Aplia Assignment is due before 5
PM on Tuesday, November 20
35
Exam Schedule is now
available


Tuesday December 4
9:30 – 12:30
36
Format of Exam

Section A (100 marks)
– 20 MCQ
– Select no more than one option for each question
and carefully follow the instructions on the MCQ
answer sheet. For each question in Section A, you
will receive 5 marks for a correct answer, –1.25
marks for an incorrect answer and a mark of 0 if
the question is not answered.

Section B (200 marks)
–
–
–
–
Answer 3 of the following 5 questions.
Each question is worth equal marks.
Each question has 4-5 different parts
There are no long essay questions
37
How prepare for exam?
1.
Study all the assigned chapters of both books
 Chapters 1-11 of Baye
 Chapter 8 of Frank
 Paper by Jensen
2.
3.
4.
5.
6.
7.
Work on the end of the chapter questions.
Study notes/ my slides on my webpage and Brendan’s
slides on blackboard
Review all Aplia questions.
Three sample exams are posted on blackboard.
Review previous exams especially 05/06
Attend the Review Session that has been scheduled
for 7 p.m. in O'Flaherty Theatre. On Monday,
November 19
I will be here a week after the classes are finished.
38
Ask me questions.
Other issues
1.
2.
3.
4.
Only 8 of the aplia assignments will count
towards the final exam.
The 35% rule applies for Commerce
students. This means that commerce
students must get 35% in the final exam
before their assignment work can be
counted.
Exams of Group A & Group B are identical
Before I leave, Brendan and I will prepare
an answer key for the exam.

He will then correct all the exams according to
the key.
39
Finitely Repeated Games: Uncertain final
period
suppose
Suppose that the firms collude & charge high and
high
the
interest
rate is 0
the trigger strategy is the same (if one firm cheats
the other will charge the lower price forever)
Probability
of ending
is Φ
40
Let’s compare profits from cheating
with profits from not cheating
Set 50 =
10/Φ
and solve
for Φ
Profits are
equal if Φ=
0.2
Profits (Π) from cheating are 50.
Profits from not cheating are
10 + (1- Φ).10 + (1- Φ)2.10 +…… =
10/Φ
Profits from cheating are
greater than the profits of
cooperating if Φ > 0.2
41
Key Insight

It is more likely to sustain the collusion
if
– Preset value of cheating is less than the
present value of cooperating
Interest rates are low
 Probability of ending is low

– The ability of monitoring the action of
rivals is high

Fewer firms
– The ability of punishing the cheaters is
high

Reputation matters
42
A Pricing Game that is
repeated: known final
period







Suppose for simplicity that there are two rounds to
this game.
Both players know that the game ends after the
second period.
A trigger strategy will not work in this case.
Neither firm has an incentive to cooperate in the
last period since there is no punishment for
cheating.
Since the firms are certain to cheat in the final
round there is no incentive to cooperate in the first
round.
The result is that both firms always cheat.
The result is the same regardless of the number of
rounds.
43
A Pricing Game that is
repeated: unknown final
period


An alternative strategy is to play Titfor-tat. This means that you cooperate
on the first round and then you do
whatever the other player did in the
previous round.
Tit-for-tat strategy requirements
 Players
recall other player’s moves
 Players have a stake in future outcomes
44
Sequential (multistage)
games

An extensive-form game summarizes
– who the players are,
– the information available to the players at
each stage of the game,
– the strategies available to the players,
– the order of the moves and
– the payoffs that result from the various
strategies.
45
Sequential (multistage)
games (A has to move first)
Suppose B
threatens
that he will
choose
Down no
matter what
What is the best strategy
for A?
Chose down
Is (Down, Down) a Nash
equilibrium?
yes
Is this a reasonable outcome?
Should A believe B’s threat to choose
Down if A chooses Up?
No, this is not a reasonable outcome
46
Sequential (multistage)
games
Suppose
B’s strategy
is to
choose up
if player A
chooses up
and down
if A
chooses
down.
This leads
to the
equilibrium
(up, up).
This is
also a Nash
equilibrium.
This is a more reasonable
Equilibrium because it doesn’t
involve threats that are not
credible.
This equilibrium is a sub-game
perfect equilibrium – at each
stage of the game neither player
can improve its payoffs by changing
its strategy.
47
The Pricing to Prevent Entry
Game in Extensive Form


Suppose B is an existing firm in the
market and A is a potential entrant.
B can react to A’s entry by either
lowering price or leaving price
unchanged.
48
The Pricing to Prevent
Entry Game in Extensive
Form
-1, 1
Lower price
Enter
Incumbent (B)
Leave price
unchanged
Entrant (A)
5, 5
Stay Out
0, 10
B is threatening to lower its price if A
enters, is this a credible threat?
No
49
Is there a Nash Equilibrium
(NE)?
There are 2
NEs
-1, 1
Lower price
Enter
Entrant
(A)
Incumbent (B)
Leave price
unchanged
5, 5
Stay Out
0, 10
Yes, if B threatens to lower the
price if A enters
NE is for A to stay out
Another NE: if A enters
and B leaves price
unchanged
This is sub game
prefect NE
50