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Brighton Business School
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Level Six Examination
May/June 2014
EC364: Game Theory in Economics, Business & Finance
Instruction to candidates:
Time allowed: 2 Hours
Rubric: There are THREE sections to this examination paper
Section A: You are required to answer ONE question from Section A
Section B: You are required to answer ONE question from Section B
Section C: You are required to answer ALL PARTS of Question 5 in Section C
All questions in Sections A and B bear a maximum of 30 marks and all parts of question 5 in
Section C
bear a maximum of 4 marks.
Nature of examination: Unseen/Closed Book
Allowable material: None
Page 1 of 3
EC364: Game Theory in Econ, Fin & Bus
(May/June 2014)
Question 1
Consider the following two-player game in strategic form. Player A has four pure strategies and
Player B has six pure strategies. The payoff matrix is as follows (in each cell the first number is
player A’s payoff):
Player
A
a1
a2
a3
a4
Player B
b1
b2
3|3
0|8
1|4
4|4
5|3
6|3
7|8
7|2
b3
3|0
3|6
2|2
6|6
b4
-1|1
7|7
3|2
5|5
b5
0|0
9|5
6|0
0|6
b6
6|3
1|1
2|-2
8|8
(a)
Find all Nash equilibria in pure strategies.
(10 marks)
(b)
How would you approach the problem of finding Nash equilibria in mixed strategies? Note
that you don’t have to actually calculate those equilibria; only to explain the steps you would
take.
(10 marks)
(c)
Find the maximin solution of the game in pure strategies. Is it wise in this case to eliminate
dominated strategies?
(10 marks)
Question 2
Consider the following scenario. There are two players and both have two pure strategies. The
game has four possible consequences for both players which both rank in the following way: C1 >
C2 > C3 > C4. However, we assume that the game can be played according to two different sets of
rules that define two different games. Suppose that the two games lead to the following outcomes
depending on the strategy pairs of the players (in each cell the first C is the consequence for player
A, the second C applies to player B):
Game 1
Player
A
Game 2
Player B
b1
b2
a1 C2|C2 C4|C1
a2 C1|C4 C3|C3
Player A
Player B
b1
b2
a1 C2|C2 C2|C3
a2 C3|C2 C3|C3
Before playing the actual game, the players must obviously decide which set of rules to adopt. This
problem constitutes a ‘metagame’ and the players first must agree on the rules for this. Let us
assume that they adopt the following rule of unanimity: Game 1 or game 2 are played if and only if
both players agree to it. Otherwise, the game is called off and each player gets a status quo (or
‘reservation’) payoff C. Let us further assume that both players want to avoid the status quo.
(a)
Conceptualise the metagame in a suitable way (Hint: Note that game 1 and game 2 are
proper subgames of the metagame).
(10 marks)
(b)
Find the Nash equilibrium of the metagame. What does it mean analytically that players want
to avoid the status quo?
(10 marks)
Carefully interpret your findings in (b).
(10 marks)
(c)
Page 2 of 3
EC364: Game Theory in Econ, Fin & Bus
(May/June 2014)
Section B: You are required to answer one question from this section
Question 3
In iterated prisoners’ dilemma games the strategy ‘tit-for-tat’ has been shown to be very successful.
(a)
Explain the strategy.
(10 marks)
(b)
What are the essentials that makes tit-for-tat successful?
(10 marks)
(c)
Give examples of tit-for-tat.
(10 marks)
Question 4
‘Chicken’ (a most unfortunate name; why should chickens be less brave than other beings?) is a
simple coordination game that nonetheless is extremely relevant to many spheres of life (question
is ‘who blinks first’?).
(a)
Explain the logic of the game.
(10 marks)
(b)
How would a successful player in this game have to act.
(10 marks)
(c)
Give examples (please not from the film ‘rebel without cause’ with the fabulous James
Dean).
(10 marks)
Section C: You are required to answer all parts of this question
Question 5
Briefly explain the following terms and concepts:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Subgame perfect Nash equilibrium.
Strategy.
Tragedy of the commons.
Bayes-Nash equilibrium.
Continuous strategies game.
Iterated game.
St. Petersburg Paradox.
Expected utility.
Weakly dominant strategy.
Folk theorems in game theory.
Page 3 of 3
EC364: Game Theory in Econ, Fin & Bus
(May/June 2014)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)
(4 marks)