ECON 44115
GAME THEORY
Postgraduate Programmes 2022/23
1
SUMMATIVE ASSIGNMENT
ECON 44115 - GAME THEORY
Answer both questions
Question 1 (40 marks)
Firm 1 is currently a monopolist in industry A. In this industry, output is produced at
zero cost. The inverse demand curve is PA = 9 – QA. Firm 2 is currently a monopolist
in industry B. In this industry, output is produced at a cost of two per unit. The inverse
demand curve is PB = 14 – QB. There is no interaction between demand in the two
industries, or between costs in the two industries. Firm 3 must decide whether to enter
industry A or industry B. It must enter one, and only one, of these industries. If it enters
industry A, then firms 1 and 3 compete as Cournot duopolists, and firm 2 is a
monopolist in industry B. If firm 3 enters industry B, then firms 2 and 3 compete as
Cournot duopolists, and firm 1 is a monopolist in industry A.
(a) Provide a full characterization of all subgame perfect Nash equilibria of this game.
(25 marks)
(b) Does this game have any Nash equilibria (not subgame perfect) beyond what was
identified in part (a)? Explain your answer.
(15 marks)
Question 2 (60 marks)
Consider a bargaining game. Players 1 and 2 are bargaining over how to split £1. Both
players simultaneously announce shares they would like to have, s1 and s2, where 0
≤ s1, s2 ≤ 1. If s1 + s2 ≤ 1, the players receive the shares they announced. However, if
s1 + s2 > 1, both players receive zero.  
(a) What are the pure-strategy Nash equilibria of this game? Explain your answer. 
(15 marks) 
(b) What do you think are the issues with this game to prevent it from being used in
real life? How would you amend it so that it can be more viable to be used in real life?
Explain your answer. 
(20 marks) 
(c) Read Ernst Fehr Klaus M. Schmidt (1999) A Theory of Fairness, Competition, and
Cooperation, The Quarterly Journal of Economics, Volume 114, Issue 3, pp. 817–868.
Consider the utility function on p. 822 and suppose that α = 1 and β = 0 for both players.
What are the pure-strategy Nash equilibria of this game? Explain your answer. 
(15 marks) 
ECON 44115
GAME THEORY
Postgraduate Programmes 2022/23
2
(d) Consider the Fehr-Schmidt preferences from the above. But consider that players
can only propose multiples of £0.05, i.e., 0, 0.05, 0.10, 0.15, …, 0.95, 1. Suppose α =
5 and β = 0. What are the pure-strategy Nash equilibria of this game? Explain your
answer. 
(10 marks)
Overall word limit: 2000
SUBMISSION INSTRUCTIONS
Your completed assignment must be uploaded to Learn ULTRA
no later than 11:59am (UK time) on 24th April 2023.
It is your responsibility to back up your work. IT issues are not a valid reason
for a late submission.
You should back up your work on more than one device.
A penalty will be applied for work uploaded after 11:59am as detailed in the
Late submission policy. You must leave sufficient time to fully complete the
upload process before the deadline and check that you have received a
receipt. At peak periods, it can take up to 30 minutes for a receipt to be
generated.
Assignments should be typed, using 1.5 spacing and an easy-to-read 12-point font.
Assignments and dissertations/business projects must not exceed the word count
indicated in the module handbook/assessment brief.
The word count should:
▪ Include all the text, including title, preface, introduction, in-text citations, quotations,
footnotes and any other items not specifically excluded below.
▪ Exclude diagrams, tables (including tables/lists of contents and figures), equations,
executive summary/abstract, acknowledgements, declaration, bibliography/list of
references and appendices. However, it is not appropriate to use diagrams or
tables merely as a way of circumventing the word limit. If a student uses a table or
figure as a means of presenting his/her own words, then this is included in the word
count.
ECON 44115
GAME THEORY
Postgraduate Programmes 2022/23
3
Examiners will stop reading once the word limit has been reached, and work beyond
this point will not be assessed. Checks of word counts will be carried out on submitted
work, including any assignments or dissertations/business projects that appear to be
clearly over-length. Checks may take place manually and/or with the aid of the word
count provided via an electronic submission. Where a student has intentionally
misrepresented their word count, the School may treat this as an offence under
Section IV of the General Regulations of the University. Extreme cases may be viewed
as dishonest practice under Section IV, 5 (a) (x) of the General Regulations.
Very occasionally it may be appropriate to present, in an appendix, material which
does not properly belong in the main body of the assessment but which some students
wish to provide for the sake of completeness. Any appendices will not have a role in
the assessment - examiners are under no obligation to read appendices and they do
not form part of the word count. Material that students wish to be assessed should
always be included in the main body of the text.
MARKING GUIDELINES
Performance in the summative assessment for this module is judged against the
following criteria:
• Relevance to question(s)
• Organisation, structure and presentation
• Depth of understanding
• Analysis and discussion
• Use of sources and referencing
• Overall conclusions
The word count should include all the text (plus endnotes and footnotes), but
exclude diagrams, tables, bibliography, references and appendices. Guidance on
referencing can be found on Sharepoint; Examinations and Assessment
(sharepoint.com)
PLAGIARISM AND COLLUSION
Students suspected of plagiarism, either of published work or the work of other
students, or of collusion will be dealt with according to School and University
guidelines.
Your assignment will be put through the plagiarism detection service.
END OF ASSESSMENT