MG301-22/23-1-MASTER Academic Year 2022-2023. Continuous Assessment #1 MG301-Strategy MG301-22/23-1-MASTER MASTER VERSION Do not turn the page until instructed to do so. Your Candidate Number: Your Calculator: You have 60 minutes. This is a multiple-choice quiz. Choose the one alternative that best completes the statement or answers the question. For each question there is one, and only one, valid answer. There are 25 points possible. Each question carries one point. Answer all of the questions. Indicate your answer both on the exam and on the answer sheet provided separately. You should answer in this exam by circling the letter corresponding to your answer. Use your #2 pencil to record your answer in the answer sheet. This quiz is closed book and you are allowed the use of a calculator. This quiz is given under the terms and conditions of LSE Code. MG301-22/23-1-MASTER Questions 1-8 Question 1 Suppose that after a process of iterated deletion of WEAKLY dominated strategies, you arrive at a single profile of strategies. Which of these statements concerning this profile of strategies is not always true? a. b. c. d. Question 2 d. The best response of that player always includes A, but may include other strategies. A player could have other strategies that are weakly dominated, but not dominated. The player will always play A only if she knows other players are rational. If she suspects other players to be irrational, she may play a different strategy. If the player is not rational, she may not play A. If an industry is comprised of four firms and their market shares are 0.40, 0.30, 0.20 and 0.10, then the Herfindahl index (where the theoretical maximum is 1) is a. b. c. d. e. Question 6 the payoffs earned by the players are the same. each player has a dominant strategy. there is no other profile of strategies which gives the same payoffs to the players. at least one player has a profitable deviation. even after watching the rival’s choice, a player would not profit from changing his/her intended strategy. Suppose that a player has a dominant strategy A. Which of the following statements is true? a. b. c. Question 5 Yes, but only if the others bid less than 40. No, because he sometimes loses. No, because he can do better by outbidding others. Actually, 40 is a dominant strategy. Yes, he cannot do better by changing his strategy. In a pure-strategy Nash equilibrium a. b. c. d. e. Question 4 If any player has a dominant strategy, it would include it in this profile of strategies. This outcome would not have survived if instead we had deleted only dominated strategies. It is a Nash equilibrium. It is the unique Nash equilibrium. Eric values a set of golf clubs at 40. In a second price auction for these clubs, is bidding 40 a weakly dominant strategy? a. b. c. d. e. Question 3 Definitions 0.1 0.2 0.3 0.4 0.5 In comparing the Cournot equilibrium with the perfectly competitive equilibrium a. b. c. d. both profit and price are higher in Cournot. both profit and price are lower in Cournot. profit is higher and price is lower in Cournot. profit is lower and price is higher in Cournot. MG301-22/23-1-MASTER Question 7 Suppose that n firms offer a homogenous good to consumers. Market demand is downward sloping, and all firms have the same (constant) marginal cost. If firms compete by simultaneously setting prices, then which statement is false? a. Total industry profits are lower with 𝑛 > 1 firms compared to the case that there is a single firm. b. Firms exert a positive externality on each other; as a result, whenever 𝑛 > 1, if all were to raise prices relative to the equilibrium prices, profits would increase. c. For 𝑛 > 2, increasing the number of firms strictly lowers equilibrium prices. d. Prices would be lower if all firms’ marginal cost would be strictly lower. Question 8 If firm 1 and firm 2 are competing simultaneously in prices and have access to the same production technology: a. b. c. d. e. Questions 9-11 firm 1 will react to a price increase by firm 2 by raising its own price when products are substitutes. each firm does not internalize the effect on rivals of changing its price when setting prices. firm 1 will react to a price increase by firm 2 by reducing its own price when products are complements. less differentiation leads to more aggressive pricing by firms. all of the above. Game Theory: Splitting a Prize Two siblings (1 and 2) will battle for a money prize under the following conditions. Each of them must simultaneously announce a real number between 0 and 10 (both inclusive); that is, sibling 1 names his desired number n1, (0 ≤n1≤10) and sibling 2 chooses his number n2 (0 ≤n2≤10); if n1+n2≤8, then the players get their demands (and their mom will take any leftover money). If n1+n2>8, then the players get nothing (and their mom keeps all the money). Assume that each sibling cares only about how much money he can individually obtain, and the more the better. Question 9 If sibling 2 believes sibling 1 will choose n1=6, what is sibling 2’s best response? a. b. c. d. e. Question 10 The unique best response is 6. Any number lower than 2. The unique best response is 2. Any number is a best response. None of the above. If sibling 2 believes player 1 will choose 10, what is sibling 2’s best response? a. b. c. d. e. The unique best response is 0. The unique best response is 10. Both 0 and 10 are the only best responses to n1=10. Any number is a best response. None of the above. MG301-22/23-1-MASTER Question 11 Which of the following statements about Nash equilibrium in this game is TRUE? a. b. c. d. Any pair of numbers in which each is smaller than 8 is a Nash equilibrium. Any pair of numbers in which one player plays 8 and the other player a number lower than 8 is a Nash equilibrium. Only pair of numbers that add up 8 are Nash equilibria. None of the above. Questions 12-17 Cournot Competition with many firms. Consider an industry where there are n firms, which produce identical goods. If total industry production is Q, then firms can sell their product at price P = 110-Q Suppose that these firms operate at a marginal cost of £10 and they are competing simultaneously in quantities. Suppose that firms can produce fractional units (so production could be any real number, not restricted to be an integer). Question 12 What will be market price if 𝑛 = 1? a. b. c. d. e. Question 13 What will be market price if 𝑛 = 2? a. b. c. d. e. Question 14 0 ≤ p∗ < 15 15 ≤ p∗ < 30 30 ≤ p∗ < 50 50 ≤ p∗ < 70 70 ≤ p∗ What will be market price if 𝑛 = 200? a. b. c. d. e. Question 15 0 ≤ p∗ < 15 15 ≤ p∗ < 30 30 ≤ p∗ < 50 50 ≤ p∗ < 70 70 ≤ p∗ 0 ≤ p∗ < 15 15 ≤ p∗ < 30 30 ≤ p∗ < 50 50 ≤ p∗ < 70 70 ≤ p∗ Suppose that demand increases, so that if total production is Q, firms obtain a price P = 510-Q. What will be market price if 𝑛 = 200? a. b. c. d. e. 0 ≤ p∗ < 15 15 ≤ p∗ < 30 30 ≤ p∗ < 50 50 ≤ p∗ < 70 70 ≤ p∗ MG301-22/23-1-MASTER Question 16 Suppose that inverse demand is still given by P = 110-Q, but because of worldwide problems in the supply chain, all firms marginal costs increase from £10 to £30. What will be market price if 𝑛 = 200? a. b. c. d. e. Question 17 0 ≤ p∗ < 15 15 ≤ p∗ < 30 30 ≤ p∗ < 50 50 ≤ p∗ < 70 70 ≤ p∗ In this setup, a. b. c. d. e. the Bertrand equilibrium results in the same output but a lower price than in the Cournot model. the Bertrand equilibrium results in a smaller output but a lower price than in the Cournot model. competition is fiercer than if instead they competed by simultaneously setting prices. each firm imposes a negative externality on others, and they will end up charging a lower price than a monopolist will do. each firm imposes a positive externality on others, and they will end up charging a lower price than a monopolist will do. Questions 18-22 Price Competition with differentiated products Two firms (1 and 2) are competing in an industry with differentiated products. Their demand functions are given by q1 = 140 – 2 p1 + p2 q2 = 100 – 2 p2 + p1 where p1 and p2 the prices charged by each firm, respectively, and q1 and q2 are the resulting demands. Assume that both firms have marginal cost equal to 0 and they are competing simultaneously in prices. Question 18 Which of the following is TRUE? a. b. c. d. e. Question 19 If firm 1 believes that firm 2 will price at p2=40, what price will firm 1 charge? a. b. c. d. e. Question 20 Products are substitutes and firms’ pricing strategies are strategic substitutes. Products are substitutes and firms’ pricing strategies are strategic complements. Products are complements and firms’ pricing strategies are strategic substitutes. Products are complements and firms’ pricing strategies are strategic complements. In a Bertrand game with differentiated products prices are always strategic complements. p1 < 15 15 £ p1 < 25 25 £ p1 < 35 35 £ p1 < 45 p1 ³ 45 If firm 2 believes that firm 1 will price at p1=40, what will be firm 2’s best response? a. b. c. d. e. p2 < 15 15 £ p2 < 25 25 £ p2 < 35 35 £ p2 < 45 p2 ³ 45 MG301-22/23-1-MASTER Question 21 If p1* and p2* denote the Bertrand equilibrium prices, how much is p1*? a. b. c. d. e. Question 22 less than 10 at least 10, but less than 30 at least 30, but less than 40 at least 40, but less than 50 above 50 If p1* and p2* denote the Bertrand equilibrium prices, how much is p2*? a. b. c. d. e. less than 10 at least 10, but less than 30 at least 30, but less than 40 at least 40, but less than 50 above 50 Questions 23-25 Game Theory: Competitive Product Design. Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below. Firm 2 Firm 1 Question 23 C A -10,-10 0,10 10,20 B 10,15 -20,-20 -5,x C 20,10 15,x 12,12 x > 15 x > - 20 x < 12 Regardless of the value of x, C is never a dominant strategy for Firm 2. None of the above. For what values of x is A a dominated strategy for Firm 2? a. b. c. d. e. Question 25 B For what values of x is C a dominant strategy for Firm 2? a. b. c. d. e. Question 24 A x > 15 x >10 x <12 Regardless of the value of x, A is never a dominated strategy for Firm 2. None of the above. For what values of x is (C, A) the unique Nash Equilibrium. a. b. c. d. e. x > 15 x <10 Regardless of the value of x, (C,A) is never a Nash Equilibrium (C,A) can be a Nash Equilibrium, but, regardless of the value of x, it can never be the unique Nash Equilibrium None of the above.
