3. Consider the same game as in the previous question and suppose both firms choose between three price levels 3, 4, and 10. (a) Suppose T = 2, and 8 = 1. Can the path ((4, 4), (4, 4)) be implemented in a SPNE? (e) Suppose T = ∞0, and 8 € (0, 1). For which 8 can the path ((4, 4), (4, 4), ...) be implemented in a SPNE using grim trigger strategies?
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- Problem 3. Consider the following game with three firms. First, firms 1 and 2 si- multancously choose quantities q1 and q2 respectively. After observing firm 1 and 2's quantities, firm 3 chooses its quantity q3. There is no production cost and the inverse demand function is p= 12 – (91 +2 + 93). (a) Compute the SPNE of this game. (b) Give an example of Nash equilibrium s* with s = 4 and s, = 6 , that is not subgame perfect. game theory question3. The following is an interpretation of the rivalry between the United States (USA) and the Soviet Ünion (USSR) during the cold war. Each side has the choice of two strategies: Aggressive and Restrained. The payoff table is given as follows: USSR Restrained Aggressiveness Restrained 4,3 1,4 USA Aggressiveness 3,1 2,2 a) Consider this game when the two countries move simultaneously. Find all pure strategy Nash equilibria. b) Next consider three alternative ways in which the game could be played with sequential moves: (i) The USA moves first and the USSR moves second. (i) the USSR moves first and the USA moves second. (i) The USSR moves first, and the USA moves second, but the USSR has a further move after the USA moves. For each case, draw the game tree and find the subgame-perfect Nash equilibrium. c) What are the key strategic issues (commitment, credibility and so on) for the two countries. (Note: Be concise. Your answer should not exceed 300 words].Suppose two firms A and B compete against each other in a Cournot fashion by choosing their quantities. What is the Nash Equilibrium of the game if both firms have a constant marginal cost of 2 and the price in the market is: p(qa + qB) = 20 – 2(qA + qB). O (3, 3) O (2, 2) O (4, 4) None of the other answers are correct (5, 5)
- Starbucks and Krispy Kreme are trying to decide whether or not to open a shop in the new Mall of Africa. They both prefer if the other firm opens a shop because they can draw bigger crowds but neither wants to be the only American-branded coffee shop in the Mall. The payoff matrix for this dilemma is below. Krispy Kreme Open Don't Open Starbucks Open (i) (ii) 5,5 2,6 Don't open (iii) (iii) 6,2 3,3 MCQ question 4 Find the Nash Equilibrium (Starbucks, Krispy Kreme) for the payoff matrix when the game is played simultaneously. A. (5:5) only. B. (6,2) only. C. (2,6) only. D. (3,3) only E. There is no stable Nash Equilibrium. MCQ question 5 Suppose that Starbucks goes first in choosing to open or not to open. What is the outcome for this game? A. (5:5) only. B. (6,2) only. C. (2,6) only. D. (3,3) only E. There is no stable Nash Equilibrium.1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.
- Table 3. This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A. Profit for Firm B). Firm A Q=5 Q=6 Firm B Q=5 (24, 24) (30, 10) Q=6 (10,30) (19, 19) Refer to Table 3. The dominant strategy For Firm A is to produce Select one: O a. 5 units and the dominant strategy for Firm B is to produce 5 units. b. 5 units and the dominant strategy for Firm B is to produce 6 units. c. 6 units and the dominant strategy for Firm B is to produce 5 units. d. 6 units and the dominant strategy for Firm B is to produce 6 units.a) Clearly indicate the eliminated dominated strategies. Apply the EIE algorithm, and determine the solution set of the game in normal form. b) Assuming that each player would not choose strategies that are strictly dominated, determine the Nash equilibria of the reduced game J2 (3,1) (4, 2) (2, 0) (0, 4) (1, 5) (3,0) (1, 3) (2, 2) a J1 (4, 1) (2, 5) (2,6) (5, 2)What conditions must non-linear time series models, such as vector autoregressive models, satisfy in order to use impulse response functions
- Consider the Normal Form Game characterized in the following figure: P1\P2 X Y Z A B с (1,1) (0,0) (-1,0) (0,0) (2,2) (0,0) (0,-1) (0,0) (3,3) Which is the Strictly Dominated Strategy for player 1? O (1,0,0) O (0,1,0) O (0,0,1) There are no strictly dominated strategies for player 1You should show that the best response map gives a fixed-point in symmetric strategies help pleaseBased on the game depicted in the matrix below, which of the following is true: Player 1 U M D L 4,3 3,2 5,0 Player 2 C 6,0 8,4 9,3 R 6,2 3,6 7,4 OD is a dominant strategy for Player 1 OR is a dominant strategy for Player 2 OL is a dominated strategy for Player 2 O (D,C) is the Nash Equilibrium of the game because it has the highest combined payoff O All of the above