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Sequential games are used to analyze the situation in which one firm acts and other firms respond.
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- Micro Nash game theory Show that if in a game G, the sets of actions (A i) i in N are compact, and the payment functions (u i) i in N are continuous, then for all i in N, the application of Best response has a closed graph. Conclude that the application of best response has a closed graph.Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 9, 8 14, 14 18, 25 12, 19 B 23, 13 10, 18 14, 26 19, 21 a. What is player 1’s optimal strategy? multiple choice Strategy B Strategy A Player 1 does not have an optimal strategy. b. Determine player 1’s equilibrium payoff. PrevSuppose 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:
- 8 Please use the game theory matrix to answer the following question We have 110,000 Homes • The low price is $79.95 and the high price is 10% more • Set up fees of $49.50 + $6.50 per subscriber The company's profit is based on its price and its competitor’s price: What is the contribution margin per house in each scenario? *Contribution margin = Price – total costsUse the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 12, 11 18, 18 23, 19 6, 27 B 19, 7 3, 18 20, 12 22, 22 a. What is player 1’s optimal strategy?multiple choice Player 1 does not have an optimal strategy. Strategy A. Strategy B. b. Determine player 1’s equilibrium payoff.suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets. Capturesque Pricing High Low Padmania Pricing High 11, 11 2, 18 Low 18, 2 10, 10 For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $18 million, and Capturesque will earn a profit of $2 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms. If Padmania prices high, Capturesque will make more profit if it chooses a ______ price, and if Padmania prices low, Capturesque will make more profit if it chooses a _____ price. If Capturesque prices ______ high, Padmania will make more profit if it chooses a price, and if Capturesque prices low, Padmania will make more profit if it chooses a _____…
- Consider a small town that is served by two grocery stores, White and Grey. Each store must decide whether to stay open on Sunday or whether it will lose on that day. If both stores decide to close, then each has monthly profits of $21,000. However, if one is open and the other closed, the open one has profits of $25,000 and the closed store has profits of $17,000. If both remain open on Sundays, then each has profits of $20,000. Why might profits be lower if both are open on Sundays than if both are closed on Sundays? Does either firm have a dominant strategy? Is there a dominant strategy equilibrium? Is there a strategy for joint profit maximizing?12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s <w. If an army attacks but its rival does not, no costs are borne by either side. Identify all 12.7 Exercises • 267 the pure-strategy Bayesian Nash equilibria of this game for the following two cases, and briefly describe…Give an example of a strategic game in which at the Nash equilibrium players play lotteries. Define the game and explain the logic that leads to the equilibrium choices.
- Which one of the following statements about the circular city model is incorrect? A. This is a 2-stage dynamic game. B. In the first stage the firms simultaneously choose their locations. C. In the first stage the firms simultaneously choose whether to enter the market. D. In the second stage the firms simultaneously choose their prices.(a) Discuss how asymmetric information can influence decision-making:(i) In game theory, regarding competitors’ pricing.(ii) Between insurance companies and their clients.(b) Two hotels, Hotel Sandy and Hotel Magda, are competing for a limited number of tourists. The hotels have approval to either expand hotel operations, or add recreational water sports to their offerings. No one hotel has approval do both of these changes. A research company has determined that the following outcomes are likely:If Hotel Sandy expands, and Hotel Magda adds water sports, Hotel Sandy will increase its market share by 1%, and Hotel Magda will increase its market share by 3%.If Hotel Sandy adds water sports, and Hotel Magda expands, Hotel Sandy will decrease its market share by 5%, and Hotel Magda will increase its market share by 2%.If both hotels add water sports, Hotel Sandy will increase its market share by 4%, and Hotel Magda will increase its market share by 5%.If both hotels expand, Hotel Sandy…Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 Strategy C D E F Player 1 A 26, 19 7, 16 12, 5 19, 10 B 9, 18 16, 2 4, 14 20, 15 a. What is player 1’s optimal strategy? a)Player 1 does not have an optimal strategy. b)Strategy A. c)Strategy B. b. Determine player 1’s equilibrium payoff. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.