ECOS3012 Strategic Behaviour
Tutorial 1 questions
• You should try your best to solve these questions before coming to the tutorial.
• For the easy questions, you will be asked to share your answers with your classmates.
• For the other questions, you will be invited to share your thoughts on them (even if you
hadn’t figured out the final solution). We will discuss these questions in detail.
Q1 Two candidates (A and B) are running for president. Three voters (1, 2, and 3) are using
the majority-rule to decide which candidate is the winner. The candidate with two or
more votes wins.
Voters’ preferences are summarised by the payoff tables below.
Voters 1 and 2: candidate A > candidate B
Voter 3: candidate B > candidate A
Please find all pure-strategy Nash equilibria of this game.
voter 3: vote for A
voter 2
vote for A vote for B
voter 1
vote for A 1,1,0 1,1,0
vote for B 1,1,0 0,0,1
voter 3: vote for B
voter 2
vote for A vote for B
voter 1
vote for A 1,1,0 0,0,1
vote for B 0,0,1 0,0,1
Q2easier In the following game, which strategy pairs survive the iterated elimination of strictly
dominated strategies? Which are the pure-strategy Nash equilibria?
Player 2
L M R
Player 1
U 2,1 3,1 3,5
M 6,4 3,3 3,4
D 4,3 6,0 4,1
Q3 On the April Fool’s Day of 2017, Reddit created an extraordinary social experiment
called “Place”. The “Place” is an online canvas of 1000×1000 pixels. During a 72-hour
window, each user can colour one pixel every 5 minutes.
https://en.wikipedia.org/wiki/Place_(Reddit)
Let’s consider a simplified version of this game. Suppose there are two users, Ann
and Bob. Each user can color exactly 7 pixel squares on a canvas, and they must pick
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their pixel squares simultaneously. They can work together to draw a lovely heart (14
pixels), or work separately to draw smiley faces (each = 7 pixels). They prefer heart to
smiley face. The worst case is to draw half a heart and find out later that the other user
has drawn a smiley face. (https://www.pixilart.com/draw)
= Excellent!!!
= Good
= Sad
This scenario is qualitatively equivalent to which of the following games?
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1. Prisoners’ dilemma
2. Battle of the sexes
3. Stag hunt
4. Penalty kick
Q4easier Consider the following scenario:
You and your roommate have just entered the final round of interview with your dream
company, but there is only one position available. On the morning of the interview,
you must decide how to dress: business casual or business formal. Both you and your
roommate prefer the comfort of business casual, but if the other person dresses casually,
you want to dress formally to impress the company and boost your chance of success.
(me formal, roommate casual) > (both casual) > (both formal) > (me casual, roommate
formal).
This scenario is qualitatively equivalent to which of the following games?
1. Prisoners’ dilemma
2. Battle of the sexes
3. Stag hunt
4. Penalty kick
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