SESS0009
Applied Game Theory for Economics and Business
COURSEWORK 2024/25
Instructions:
Answer ALL questions. For each question, illustrate your knowledge of game theory concepts and models. Provide examples and detailed answers where appropriate and present the workings and thought process in full detail. UCL guidance on plagiarism and the use of AI applies as described on Moodle. You MUST include the completed Coversheet, available on Moodle, as the first page of your submission. The word count of 3000 words is based on Chapter 10.11 of the SSEES Student Handbook and applies to net text only (does not include numbers, equations, tables and figures, captions and titles, references, abstract etc.).
If you face problems in submission, please contact your Programme Administrator or [email protected].
Marking criteria:
All questions and sub-questions carry the denoted marks. Arriving at a correct result without any explanation is worth minimal marks. Marks are awarded based on i) understanding the course material and question requirements ii) showing insight and creativity iii) correctness iv) proper use of terminology, accuracy and clarity in explanation and language v) proper presentation and notation. The criteria are in random order. Computer-formatted submissions are strongly encouraged. Plots and diagrams can be hand-drawn but must be properly placed within the text and properly labelled.
Any questions must be posted on the Teams channel for AGT, not sent by email or personal message, to benefit as many students as possible.
Question 1 (10 points)
Solve the following sequential games and explain your methodology step by step, state the Nash Equilibrium (or Equilibria).
(I) Order of payoffs is (A, B) (3 points)
(II) Order of payoffs is (A, B) (3 points)
(III) Order of payoffs is (A, B, C) (4 points)
Question 2 (10 points
Find all the Nash Equilibria (pure and mixed) in the following simultaneous games and explain your methodology step by step.
(I) (3 points)
(II) (3 points)
(III) (4 points)
Question 3 (10 points)
Bertrand competition with differentiated goods. Firms 1,2 with demand functions Q1 = 10 – 3P1 + 2P2 , Q2 = 10 – 3P2 + 2P1 and marginal costs C1 = 6, C2 = 4.
i) Find the Nash Equilibrium prices, quantities and individual profits. (3 points)
ii) The firms agree to form a cartel. Find the prices, quantities, cartel profits and individual profits under the cartel agreement. (3 points)
iii) Which firm has a reason to suggest the cartel, and is the cartel sustainable or not? Depict and explain the cartel game in an appropriate way. If it is sustainable, explain. If no, explain and suggest a mechanism that can make it sustainable a) if the deal is for one period only b) if the deal is renewed each period over 5 periods. (4 points)
Question 4 (10 points)
The merchant ship Antelope, carrying silk, was wrecked upon Goodwin Sands in October 1604. The silk belonged to two Canterbury tailors but all records have been lost. The ship was insured, so the owner invites both traders to provide separate self-assessments of the value of their silk. They can declare any amount between 50 and 200 pounds, but if they disagree the trader that declared the lower amount will receive a bonus of 50 pounds on it, while the other a penalty of 50 pounds on his amount. If they agree, they both receive the stated amounts. What is the Nash equilibrium of the game? Explain and illustrate the solution, comment on the outcome and how it relates to rationality and human behaviour.
Question 5 (50 points)
Select one example (case study) from “Economics of Strategy” , available on Moodle, that relates to economics, finance, management etc and can be modelled via game theory. Only examples (case studies) in blue backgrounds may be selected and only from the book, as below.
Examples not from the book or that are not in blue backgrounds will be marked with zero (0). State the example as "Chapter X, Example Y.Y, p. ZZZ, Title".
The goal is to model the case study through a game theoretical approach and draw conclusions from modelling and subsequent analysis.
State the basic facts and intuition/subject: what feature are you modelling and why, and how does that relate to the case study?
Explain the game you construct (payoffs, setup, uncertainty, rounds etc) in full detail and justify your choices. Link the facts of the case study to the model structure. Solve the game and fully interpret and discuss your solution.
Provide the economic intuition of your result. What does it tell us about the situation, the agents/ framework and real-world actions? Further guidance:
i) Elaborate games modelling more complex cases (e.g. introducing informational asymmetry in a competitive setup) will be awarded more points, but a simple game that is solved correctly is better than a complex game solved incorrectly, or not at all. Please bear in mind that overly simplistic approaches will receive rather low marks.
ii)A case study contains different aspects and each aspect can be modelled in different ways – there is not a unique way and your model is not meant or expected to capture everything. However, the various approaches are relevant, informative or meaningful to different degrees. If you want to capture more than two aspects in your model you are welcome, but this is not required.
iii) Do NOT do any further research on the firms, do NOT cite papers/ news/ reports and do NOT collect any data. You must use only the information provided in the case study. Feel free to make assumptions, but do not overextend and do not override or misrepresent the information given.
iv) Modelling a single feature does not mean you are required to have only one tree/ table. You are encouraged to model different variations or sub-cases and explore the case study. However, be mindful of reverse-engineering.
v) Try to discuss your results to some extent and state what you can learn from your model and what insight it provides about the situation at hand.