ECON0009: INTRODUCTION TO STRATEGIC THINKING SUMMER TERM 2023
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SUMMER TERM 2023
DEPARTMENTALLY MANAGED ONLINE EXAMINATION
ECON0009: INTRODUCTION TO STRATEGIC THINKING
Assessment available from: 09:00 pm on Friday 28 April 2023
Latest submission time: 12:00 pm on Friday 28 April 2023
All timings are given in British Summer Time (BST)
Between these times you must finish and submit your completed assessment.
This is an open book examination. You may refer to your own module and revision notes and look up information in offline or online resources, for example Moodle, textbooks or online journals. However, you may not communicate with any person or persons about this assessment before the submission deadline. By submitting your coursework assignment, you confirm the work is your own. The use of the work of others, and your own past work, must be referenced appropriately. It is expected that you will have read and understood the Regulations for Students and your programme handbook, including the references to and penalties for unfair practices such as plagiarism, fabrication or falsification.
Which questions should be answered: Answer ALL FOUR questions.
Additional materials needed to complete the assessment: Calculator.
Any further instructions: Please note that the general goal of any assessment in Economics is to test students’ ability to analyse and evaluate economic problems, so that students can reach considered and appropriate conclusions, and can competently communicate the reasoning behind these conclusions. Therefore, the present open book coursework will also assess your clarity of expression, your ability to set out an argument or answer clearly and logically, as well as the overall structure and presentation of your answers (including referencing, where appropriate). Furthermore, a page limit of two pages A4 per question applies.
Submitting your assessment: When you have completed this assessment, you must submit your coursework in PDF format as a single file, uploaded to the relevant Moodle submission point.
QUESTIONS
Answer all four questions. Explain your workings and interpret your results. All questions carry equal weight.
Question 1
Three bidders, labeled 1, 2, and 3, bid for a painting in a third-price auction. The object is awarded to the highest bidder who pays a price equal to the third highest bid. Assume that bidders’ valuations for the painting are common knowledge and satisfy v1 > v2 > v3 . Suppose that ties are always broken in favour of the bidder with the lowest index.
(a) Show that the profile of bids (b1, b2, b3) = (v1, v2, v3) is not a Nash Equilibrium
of the game.
(b) Find a Nash Equilibrium (Hint: there exist Nash Equilibria in which all bidders
submit the same bid).
Question 2
Consider the following game in strategic form:
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Pl. 1 \ Pl. 2 |
L |
C |
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T |
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3,0 |
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M |
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1,1 |
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B |
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0,0 |
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(a) Eliminate the strictly dominated strategies for each player. Explain your
reasoning.
(b) Find the pure strategy Nash equilibria of this game or show that a pure
strategy equilibrium does not exist. In the latter case, find a mixed strategy Nash equilibrium, i.e. where both players randomize across two or more pure strategies.
(c) Provide one example of one economic or social phenomenon where the notion of a mixed strategy equilibrium is useful for understanding the phenomenon, setting out briefly why this is the case.
Question 3
There are two players, a seller and a buyer, and two time periods. In time period 1, the seller can make an investment I that will result in lower production cost in time period 2 (note that I can be any real number in the interval [0,1] so that 0 ≤ I ≤ 1).
In time period 2, the seller can sell one unit of her good to the buyer, who has demand for a single unit of the good, and a valuation of 9 for it. The production cost in time period 2 are given by c(I) = 3 − 2I .
In time period 2, the buyer observes the investment-level I and makes a price offer p to the seller (note that p can be any non-negative real number, so that p ≥ 0). If the seller accepts the offer, the good is produced and the buyer pays the seller the amount p in exchange for the good. If the seller rejects the offer, the good is not produced and no trade takes place.
(a) Formulate this situation as an extensive form game.
(b) Find the subgame perfect Nash equilibrium of the game. In particular, what is
the equilibrium price offer p and the equilibrium level of investment I?
(c) Compute the level of investment I ∗ that maximizes the sum of the buyer’s and the seller’s payoffs (i.e. the socially optimal level of investment). How does the equilibrium investment you found in (b) compare to I ∗ ? Interpret your findings.
Question 4
Two players 1 and 2 bargain to determine how to split £1. The rules are as follows: the game begins in period 1: player 1 offers an amount (a real number between 0 and 1) that she is willing to leave to player 2. Player 1’s cost of making the offer is c e (0,1) . Player 2 may accept or reject player 1’s offer. If player 2 accepts, then the proposed split is implemented immediately and the game ends. If player 2 rejects the offer, nothing happens until period 2. In period 2, the players’ roles are reversed, with player 2 making an offer to player 1 at cost c , and player 1 then choosing whether to accept or reject the offer. If player 1 accepts, the proposed split is implemented; if player 1 rejects the offer, the bargaining process is terminated and the players each receive nothing (but are left to bear any costs incurred).
(a) Formulate this situation as an extensive form game.
(b) What is the subgame perfect equilibrium of the game?
(c) Suppose now that there is an additional round of negotiations. I.e. if in period 2 player 1 rejects the offer made by player 2, bargaining proceeds into period 3. In period 3, it is again player 1’s turn to make an offer at a further cost of c . If the offer is accepted, the proposed split is implemented; if not, bargaining is terminated and the players each receive nothing (but will bear any costs incurred). What is the subgame perfect equilibrium of this variant of the game? Compare the equilibrium split and the players’ payoffs in (b) and (c).
2023-04-19