UNIVERSITY OF EAST ANGLIA
School of Economics
Main Series UG Examination 2015-2016
STRATEGIC THINKING
ECO-5004A
Time allowed: 2 hours
Answer THREE questions.
Notes are not permitted in this examination.
Do not turn over until you are told to do so by the Invigilator.
ECO-5004A
Module Contact: Arnold Polanski (ECO)
Copyright of the University of East Anglia
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1
Imagine you are a farmer. A group of nearby farmers are constructing
an irrigation and flood-control project from which you will benefit. Using game
theory, explain how you would make a decision as to whether to contribute to
the project or not.
[34 marks]
2
Explain how the prisoner’s dilemma game can help us to understand
actions taken by countries involved in the Kyoto protocol. Does modelling the
Kyoto treaty in this way suggest there is no hope for climate change treaties?
[33 marks]
3
Consider a game in which player 1 first selects between In and Out. If
payer 1 selects Out, then the game ends with the payoff vector (x,1) (x for player
1), where x is some positive number. If player 1 selects In, then this selection
is revealed to player 2 and then the players play the battle-of-the-sexes game
in which they simultaneously and independently choose between A and B. If
they both choose A, then the payoff vector is (3,1). If they both choose B, then
the payoff vector is (1,3). If one player chooses A and the other B, then the
payoff vector is (0,0).
a) Represent this game in the extensive and normal form.
[8 marks]
b) Find the pure-strategy Nash equilibria as a function of x.
[9 marks]
c) Find the pure-strategy subgame perfect equilibria when x = 2.
[8 marks]
d) Are there any pure-strategy Nash equilibria that are not subgame perfect
when x = 1/2 and when x = 7/2? (If there are, then describe them.)
[8 marks]
TURN OVER
ECO-5004A
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In the ultimatum game, the proposer offers a share of a given surplus to
the responder who can accept or reject the offer. In experimental tests of this
game, proposers rarely offer a tiny share and responders sometimes reject
positive offers. Many scholars conclude that players care about more than their
own monetary rewards. Specifically, suppose that in the ultimatum game over
a unit surplus, the responder’s actual utility payoff is given by y + α(y-z), where
y  [0,1] is the responder’s monetary reward, z  [0,1] is the proposer’s
monetary reward, z + y = 1, and α ≥ 0 is a constant. That is, the responder
cares about how much money she gets and also about relative monetary
rewards. Assume that the proposer cares only about his monetary payoff z and
that both players earn zero if the proposer’s offer is rejected.
a) Represent this ultimatum game in the extensive form (including the
payoffs).
[9 marks]
b) Find the subgame perfect equilibrium and describe how it depends on α.
[9 marks]
c) What is the equilibrium monetary split when α = 0? Explain why this is
the case.
[7 marks]
d) What is the equilibrium monetary split as α becomes large? Explain why
this is the case.
[8 marks]
END OF PAPER
ECO-5004A
Version 1
ECO-5004A
Strategic Thinking Exam Feedback
(2015-16)
In writing this year’s exam paper, we sought to achieve an even balance between ‘problemsolving’ and discursive elements, and to include elements from most topics covered on the
module. The paper very much reflected our teaching philosophy on the module: the aim was
to generously reward students who were willing and able to think deeply about the topics, but
to provide relatively little reward for rote-learning or shallow understanding.
The average mark was 58.2 (SD 8.98). The mark distribution is given in the table below.
40-49
3
50-59
11
60-69
8
70-79
4
Question-Specific Comments
Question 1:
In this question students did usually identify the Public Goods games as the relevant game
here. High marks were not achieved where students did not include e.g. some of the graphs
from the lecture notes describing why we might have a collective action problem, did not
adequately describe why we might expect a collective action problem or did not give much
detail about what a collective action problem is.
% students answered: 88.5%,
Average % Mark: 56.5%
Question 2:
Most people defined a good prisoner’s dilemma game although some did make an explicit
link between it and how it relates to the Kyoto protocol. Many people identified the
importance of the Folk theorem but some did not give sufficient details to show
understanding rather than repetition.
% students answered: 84.6%,
Average % Mark: 61.2%
ECO-5004A
Strategic Thinking Exam Feedback
(2015-16)
Question 3:
This question was not particularly well answered on the whole. It showed that the
representation of a game and finding its (subgame perfect) equilibria present difficulties for
non-trivial interactions. For example, in part a) the extensive form was mostly correctly
drawn as:
However, only a few students were able to derive the correct normal form:
1
\
2
A
B
OA
x,1
x,1
OB
x,1
x,1
IA
3, 1
0, 0
IB
0, 0
1, 3
In part b), the main difficulty presented the parameter “x”. From the table above, it can be
easily seen that Nash equilibria (NE) depend on x. For example, when x = 2, then (IA, A) is a
NE but (OA,A) is not, while for x = 5 it is the other way round.
Also many answers to parts c) and d) were rather disappointing.
% students answered: 92.3%,
Average % Mark: 51.2%
Question 4:
Somehow surprisingly, this question had (on average) the best answers which is reflected in
the high average mark.
There is no clear pattern regarding the committed mistakes, which – in any case – were of a
less serious nature.
% students answered: 34.6%,
Average % Mark: 64.2%