ECON 101 Tutorial: Week 8
Shane Murphy
s.murphy5@lancaster.ac.uk
Office Hours: Monday 3:00-4:00 – LUMS C85
LUMS Maths and Stats Help (MASH)
Centre
Are you mystified by maths? Stuck with
statistics? The LUMS Maths and Stats Help
(MASH) Centre for LUMS undergraduate
students opens this week. Every Monday (16.0018.00) and Friday (10.00-12.00), you can drop-in
to LUMS B38a or book an appointment to see a
student mentor and get help with maths and
stats
Outline
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Roll Call
Bonus
Problems
Discussion
Bonus
• Box of Lies
–
–
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–
–
–
–
–
–
Melissa McCarthy
Emma Stone
Kate Hudson
Channing Tatum
Tina Fey
Jennifer Lawrence
Julie Bowen
Kerry Washington
Kate Hudson
• You pick
Exercise 1
“If a player has a dominant strategy in a
simultaneous-move game, then she is sure to get her
best possible outcome”. True or false? Explain and
give an example of a game that illustrates your
answer.
False. The Prisoner’s Dilemma is a counter example.
Exercise 2
Consider the following simultaneous game:
Player A\B
Up
Down
Left
3, 3
2, 2
Right
5, 1
4, 4
• Find the Nash equilibrium or equilibria.
– A – up; B – left
• Which player, if any, has a dominant strategy?
– A – up; B – none
• Write down the extensive form for this game, played with
simultaneous moves.
• Suppose the game is now sequential move, with A moving
first and then B. Write down the extensive form for this
sequential move game.
• Write down the normal form for the sequential move game.
Find all the Nash equilibria.
Exercise 2
Consider the following simultaneous game:
Write down the normal form for the sequential
move game. Find all the Nash equilibria.
Player A\B
Left|Up;
Left|Down
Left|Up;
Right|Down
Right|Up;
Left|Down
Right|Up;
Right|Down
Up
Down
3, 3
2, 2
3,3
4,4
5, 1
4, 4
5,1
4,4
There are 2 Nash Equilibria:
• A Up and B Left Up, Left Dawn
• A Down and B Left Up, Right Down
– This is also a subgame perfect equilibrium
Exercise 3
Two classmates A and B are assigned a group project. Each
student can choose to Shirk or Work. If one or more players
choose Work, the project is completed and gives each student
some credit valued at 4 payoff units each. The cost of
completing the project is that 6 total units of effort (measured
in payoff units) are divided equally among all the players who
choose to Work and this is subtracted from their payoffs. If
both Shirk, they do not have to expend any effort but the
project is not completed, giving each a payoff of 0. The teacher
can only tell whether the project is completed and not which
students contributed to it
Player A\B Shirk
Work
• Find the NE
– Both Shirk
Shirk
Work
0,0
-2,4
4,2
1,1
• Find the Dominant Strategy, what game is this similar to?
– Shirk for both: This is equivalent to the PD
Exercise 3
Two classmates A and B are assigned a group project. Each
student can choose to Shirk or Work. If one or more players
choose Work, the project is completed and gives each student
some credit valued at 4 payoff units each. The cost of
completing the project is that 6 total units of effort (measured
in payoff units) are divided equally among all the players who
choose to Work and this is subtracted from their payoffs. If
both Shirk, they do not have to expend any effort but the
project is not completed, giving each a payoff of 0. The teacher
can only tell whether the project is completed and not which
students contributed to it
Player A\B Shirk
Work
• Find the NE
– Both Shirk
Shirk
Work
0,0
-2,4
4,2
1,1
• Find the Dominant Strategy, what game is this similar to?
– Shirk for both: This is equivalent to the PD
Exercise 4
Verify the following game is a version of the
Prisoner’s Dilemma
Player A\B
Confess
Silent
Confess
0, 0
3, -1
Silent
-1, 3
1, 1
Exercise 5
I’m not comfortable teaching this, luckily we are low
on time and can skip it.
Exercise 6
Identify Nash equilibria in pure strategies (if any) and
explain your findings. In particular, consider whether
players know which (if any) Nash equilibrium will result.
Firm 2\Firm 1
Do not enter
Enter
Do not enter
0, 0
0, 1
Enter
1, 0
-1, -1
Two NE:
Firm 1 Enters, Firm 2 does not
Firm 2 Enters, Firm 1 does not
Without collusion, we don’t really expect either to occur.
Exercise 7
a) Belgium has few traffic signs or signals and does not have a
give-way rule. A driver in Belgium who stops to look both
ways at an intersection loses the legal right to go first.
Using the Game of Chicken, explain why Belgium has more
per capita accidents at unmarked intersections resulting in
bodily injury compared to neighbouring countries which
have more stop signs and traffic lights and explicit rules
about right of way.
What?!? In America we have stoplights. This question is crazy
b) When a man and a woman approach a door at the same
time, it is customary for the man to let the woman go first.
Use the Game of Chicken to explain this social convention.
What?!? I don’t see gender. I only see souls.
Exercise 8
BA\Air France
QB =96
64
QA = 96
64
48
0, 0
3.1, 2
4.6, 2.3
2, 3.1
4.1, 4.1
5.1, 3.8
Above is the48normal-form representation
of a game
British
and Air
2.3, 4.6
3.8, between
5.1
4.6,Airways
4.6
France where each chooses between three possible actions: fly 96, 64 or 48
thousand passengers between Manchester and Paris, with payoffs as £m profits per
quarter.
a) Is there a strictly dominant strategy for this game?
No.
b)
c)
Use iterated elimination of strictly dominated strategies to find an outcome for
the game
AF’s QA=96 is strictly dominated by QA = 64
BA’s QB = 96 is strictly dominated by QB = 64
From what remains, 48 is dominated by 64 for each firm.
So the equilibrium is QA = QB = 64
List the assumptions you made to discover the game outcome.
The iterated approach relies on:
•
•
•
•
the belief that players won’t choose strictly dominated strategies.
Players possess common knowledge that they are payoff maximising
Players know that other players are payoff maximizing
etc
Exercise 9
The entrant moves first and the incumbent observes the entrant’s decision. The
entrant can choose to either enter the market or remain out of the market. If the
entrant remains out of the market then the game ends and the entrant receives a
payoff of 0 while the incumbent receives a payoff of 2. If the entrant chooses to enter
the market then the incumbent gets to make a choice. The incumbent chooses
between fighting entry or accommodating entry. If the incumbent fights the entrant
receives a payoff of -3 while the incumbent receives a payoff of -1. If the incumbent
accommodates the entrant receives a payoff of 2 while the incumbent receives a
payoff of 1. Solve this game.
Exercise 9
The entrant moves first and the incumbent observes the entrant’s decision. The
entrant can choose to either enter the market or remain out of the market. If the
entrant remains out of the market then the game ends and the entrant receives a
payoff of 0 while the incumbent receives a payoff of 2. If the entrant chooses to enter
the market then the incumbent gets to make a choice. The incumbent chooses
between fighting entry or accommodating entry. If the incumbent fights the entrant
receives a payoff of -3 while the incumbent receives a payoff of -1. If the incumbent
accommodates the entrant receives a payoff of 2 while the incumbent receives a
payoff of 1. Solve this game.
Entrant
Enter
Don’t Enter
Incumbent
I: 2, E: 0
Fight
I: -1, E: -3
Accomodate
I: 1, E: 2
Exercise 9
The entrant moves first and the incumbent observes the entrant’s decision. The
entrant can choose to either enter the market or remain out of the market. If the
entrant remains out of the market then the game ends and the entrant receives a
payoff of 0 while the incumbent receives a payoff of 2. If the entrant chooses to enter
the market then the incumbent gets to make a choice. The incumbent chooses
between fighting entry or accommodating entry. If the incumbent fights the entrant
receives a payoff of -3 while the incumbent receives a payoff of -1. If the incumbent
accommodates the entrant receives a payoff of 2 while the incumbent receives a
payoff of 1. Solve this game.
Entrant
Enter
Don’t Enter
Incumbent
I: 2, E: 0
Fight
I: -1, E: -3
Accomodate
I: 1, E: 2
Exercise 9
The entrant moves first and the incumbent observes the entrant’s decision. The
entrant can choose to either enter the market or remain out of the market. If the
entrant remains out of the market then the game ends and the entrant receives a
payoff of 0 while the incumbent receives a payoff of 2. If the entrant chooses to enter
the market then the incumbent gets to make a choice. The incumbent chooses
between fighting entry or accommodating entry. If the incumbent fights the entrant
receives a payoff of -3 while the incumbent receives a payoff of -1. If the incumbent
accommodates the entrant receives a payoff of 2 while the incumbent receives a
payoff of 1. Solve this game.
Entrant
Enter
Don’t Enter
Incumbent
I: 2, E: 0
Fight
I: -1, E: -3
Accomodate
I: 1, E: 2
Discussion
• Box of Lies
– Melissa McCarthy
– Emma Stone
– Kate Hudson
– Channing Tatum
– Tina Fey
– Jennifer Lawrence
– Julie Bowen
– Kerry Washington
– Kate Hudson
• You pick again!