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- Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.You have just played rock, paper, scissors with your friend. You chose scissors and he chose paper, so you won. Is this a Nash equilibrium? Explain why or why not.Suppose China and the US are deciding whether to join an international agreement to mitigate climate change. The matrix below contains payoffs that represent each country’s net benefit from their decisions. Use this information to answer Question 24. CHINA USA Join Agreement Do Not Join Agreement Join Agreement (100,100) (0,125) Do Not Join Agreement (125,0) (25,25) [24] What does each country decide to do in a Nash equilibrium? AND What is the efficient outcome? Nash: Efficient:
- Hi this is from a textbook. Thank you. Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 5 and John has a payoff of 4. If Sally plays T and John R, Sally’s payoff is 8 and John gets 3. If Sally Chooses B and John L, the payoffs are 3 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 7 to Sally and 0 to John. Which statement is true? a) The Nash equilibrium is (B,R); this is a prisoners’ dilemma b) The Nash equilibrium is (T,R); this is a prisoners’ dilemma c) The Nash equilibrium is (T,R); this is not dominant strategy equilibrium d) The Nash equilibrium is (T,L); this is a dominant strategy equilibrium e) None of the aboveImagine that two firms in two different countries want to bring a new product tomarket. Due to economies of scale, if both firms do this, they will both lose £50million. But if only one firm does this, it will gain £300 million.(a) What is the best strategy for firm A, if firm B has not yet entered the market, andwhy?(b) Illustrate this with a game theory diagram, showing appropriate payouts.(c) What is the welfare-maximising strategy for a government, and why?Consider a game where each player picks a number from 0 to 60. The guess that is closest to half of the average of the chosen numbers wins a prize. If several people are equally close, then they share the prize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30;(C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization.
- Economics: Industrial Economics Question: 1 Consider the following simultaneous move game: Player 1 selects rows and player 2 selects columns in a simultaneous move game. For every outcome, payoffs for player 1 are given by the first entry and payoffs for player 2 by the second. P1\P2 | A | B | C | D | 1 | (5,5) | (7,4) | (7,5) | (1,2) | 2 | (7,2) | (7,3) | (5,1) | (2,3) | 3 | (1,2) | (6,9) | (8,0) | (8,8) | The Nash Equilibrium is: Choices: A. (2,B) B. (3,D) C. (3,B) D. (1,C) Question: 2 In the patent pooling model, if there are four inputs that are required for production of the final goods and each one is produced by a patent-holding monopolist then 1. At the Nash Equilibrium the Lerner Index for the industry isChoices: A. Half as high as the Lerner index that would arise...B. Twice as high as the Lerner Index that would arise...C. Four times higher than the Lerner Index that we...D. Four times lower than the Lerner Index that we... 2. If the market for the final good were a…Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…Consider the following game:
- parameter z= 1 In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs tothe two players?Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays upUse the following payoff matrix for a one-shot game to answer the accompanying questions. A 5,5 0, -200 B -200, 0 20, 20 Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Which of these outcomes would you consider most likely? Explain. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter, and what outcome do you think would occur as a result?