CF963 Computational Models in Economics and Finance
Reassessment II, 2018/19
Lecturer: Maria Kyropoulou
• Answer all (four) questions below. Submit your answers to FASER by noon on the 25th March
2020. You need to submit:
– all MATLAB files that you created in the context of this assignment.
Submit them separately if possible (do NOT .zip). Make sure that your code is easy to follow, and
copy and paste your code in the report as requested in the specific tasks.
• Your assignment will be assessed on the quality of the files you submit –correctness, work quality
and quality of presentation– and how clearly you explain what you have done. Aim for precise and
concise answers and explanations. Good luck!
Your task is to design a trading strategy and test it with MATLAB on any of the FTSE 100 stocks –
daily closing prices that were provided in the module.
In your report, you need to describe your algorithm precisely in words as well as copy and paste
your MATLAB code. You should explain how you evaluate the effectiveness of your strategy, e.g. show
clearly when your algorithm buys and sells, and what profit or loss it makes in each deal (and in total).
You will not be assessed on the profits of your strategy, however, your strategy should be sophisticated
enough to demonstrate some synergy between computation and finance in this context. You should also
briefly elaborate on that synergy.
a. (13%) Consider the Cournot duopoly model where the inverse demand function and the cost functions
are given by
P = 100 −
Q
2
, c1 = 5q1, c2 =
q
2
2
2
,
where Q = q1 + q2 is the total production quantity and qi
is the production quantity of firm i, for
i = 1, 2. Give the profit functions of the firms and compute the Nash equilibrium defined by the
quantity each firm chooses to produce. Compute the profit of each firm, the consumer surplus, and
the total surplus at equilibrium.
b.(7%) Consider the leader-follower duopoly model with the inverse demand function and the cost functions
as defined in Part a. Let the reaction function of firm 2 be
r2(q1) = 50 −
q1
4
.
Give the profit function of firm 1 and find the equilibrium strategies (production quantities) of the
firms.
1
Consider the following sponsored search auction instance I:
• 3 slots. The top slot has a known click-through rate (CTR) ctr1 = 1, the middle slot has a known
click-through rate ctr2 = 0.55071 and the bottom slot has a known click-through rate ctr3 = 0.4704.
• 3 advertisers. Let the (private) value-per-click of advertiser 1 be 100000 (in some currency), the
(private) value-per-click of advertiser 2 be 52960 and the (private) value-per-click of advertiser 3
be 14583.
• The payoff of bidder i in slot j is ctrj (vi − pj ), where pj is the price charged per-click in slot j.
Under the Generalized Second-Price (GSP) auction rule:
– Advertisers are asked to declare their value per click (this doesn’t mean that their declarations are
truthful!). Advertisers are then ranked according to their declarations and the advertiser with the
highest declaration is assigned to the slot with the highest CTR, the advertiser with the second
highest declaration is assigned to the slot with the second highest CTR, and, finally, the advertiser
with the lowest declaration is assigned to the slot with the smallest CTR. For j = 1, 2, the per-click
payment pj at slot j, is set to be equal to the declaration of the advertiser assigned to slot j + 1,
while p3 = 0.
a. [4% ] Compute the optimal/highest social welfare in I.
b. [21% ] Write MATLAB code that computes a pure Nash equilibrium in I, when advertisers can declare
one of the following: 0, their true value-per-click, half of their true value-per-click.
You can (or not) follow a brute-force approach, i.e. consider all possible combinations of declarations
and for each of them check if it is an equilibrium. Copy and paste your MATLAB code in your report,
and explicitly mention where in your MATLAB code you guarantee that the equilibrium conditions are
satisfied (even if your code doesn’t run or doesn’t compute an equilibrium). If your code successfully
computes an equilibrium, present the equilibrium that you have computed in the report and mention its
social welfare. Marks will be awarded for partially-correct approaches.
Pick one of the following papers and provide a summary and critical assessment of it, by focusing on the
real life setting that is considered, the modelling choices that were made in an attempt to abstract it
and analyse it, and elaborate on the particular computational modelling technique that is applied to it.
Suggestions for points to address: What simplifying assumptions are made? How does computational
thinking help us analyze this particular situation? Are the assumptions made and/or the methodology
used appropriate? How could this analysis be extended, e.g. can you think of an adaptation to the model
that would be meaningful?
Length guide: Your answer should not exceed an A4 page overall. Aim for half page summary of the
paper and another half page for criticism on the approach. There is no need to focus on the technical
details (mathematical proofs).
Papers:
Complexity of Stability in Trading Networks, by Tam´as Fleiner, Zsuzsanna Jank´o, Ildik´o Schlotter,