Suppose that Firm A and Firm B are independently deciding whether to sell at a low price or a high price. The payoff matrix below shows the profits per year for each company resulting from the two price options. Firm B High Price Firm B Low Price $5 million $2 million $3 million $1 million $4 million $5 million $2 million $3 million a. Does Firm A have a dominant strategy? O The dominant strategy for Firm A is a low price. O No, there is no dominant strategy for Firm A. O The dominant strategy for Firm A is a high price. b. Does Firm B have a dominant strategy? O The dominant strategy for Firm B is a low price. O The dominant strategy for Firm B is a high price. O No, there is no dominant strategy for Firm B. Firm A Low Price Firm A High Price

Suppose that Firm A and Firm B are independently deciding whether to sell at a low price or a high price. The payoff matrix below shows the profits per year for each company resulting from the two price options. Firm B High Price Firm B Low Price $5 million $2 million $3 million $1 million $4 million $5 million $2 million $3 million a. Does Firm A have a dominant strategy? O The dominant strategy for Firm A is a low price. O No, there is no dominant strategy for Firm A. O The dominant strategy for Firm A is a high price. b. Does Firm B have a dominant strategy? O The dominant strategy for Firm B is a low price. O The dominant strategy for Firm B is a high price. O No, there is no dominant strategy for Firm B. Firm A Low Price Firm A High Price

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 10E

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Is the game shown by Figure 11.3 in the chapter (not this appendix) a zero-sum game or is it a positive-sum game? How can you tell? Are there dominant strategies in this game? If so, what are they? What cell represents a Nash equilibrium and why? Explain why it is so difficult for Uptown and RareAir to achieve and maintain a more favorable cell than the Nash equilibrium in this single-period pricing game.
Suppose that there are two firms in a market, firm 1 and firm 2. The marketis declining in size. The game starts in period 0, and the firms can compete in periods 0, 1,2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equalto 105 −10t, and they are 10.5 −t for firm 2. Monopoly profits (those if a firm is the onlyone left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of eachperiod, each firm must decide either to “stay in” or “exit” if it is still active (they do sosimultaneously if both are still active). Once a firm exits, it is out of the market forever andearns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits.What is this game’s subgame perfect Nash equilibrium?
5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.
Use the following payoff matrix to answer the following questions. (LO2) Player 2 Strategies C D Player 1 A −10, −10 200, −100 B −100, 220 140, 180cSuppose this is a one-shot game: a. Determine the dominant strategy for each player. If such strategies do not exist, explain why not. b. Determine the secure strategy for each player. If such strategies do not exist, explain why not. c. Determine the Nash equilibrium of this game. If such an equilibrium does not exist, explain why not.
Next, explain how it can be applied to the decisions that have to be made in an oligopoly. What specifically is the decision to be made by each seller in an oligopoly? How does each possible outcome in the prisoners' dilemma map into an outcome in an oligopoly? What do you think each seller's dominant strategy will be? Examine and discuss how the role of communication, specifically the lack of communication, can lead to an outcome that is worse for the players. (Of course, it is against U.S. law for the sellers to conspire to make the market less competitive!) Can you think of other examples of how the prisoners' dilemma could be applied to business decision making? Discuss any other applications of a prisoners' dilemma game you find to be interesting, whether from the text or one you can think of on your own.
4 Consider an extensive game where player 1 starts with choosing of two actions, A or B. Player 2 observes player 1’s move and makes her move; if the move by player 1 is A, then player 2 can take three actions, X, Y or Z, if the move by player 1 is B, then player 2 can take of of two actions, U or V. Write down all teminal histories, proper subhistories, the player function and strategies of players in this game.
Question 3 options: Now consider the same industry but assume that two firms with the same cost function c ( q i ) = 2 ∗ q i f o r i ∈ { 1 , 2 } are active in this market. What is the price that realizes when they set prices in a simultanous move game (ie they play Bertrand). Assume now that the cost of the second firm is instead c ( q 2 ) = 5 ∗ q 2 What is the equilibrium price if they again play Bertrand? (round to the nearest whole number)
Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 1 Player 2 Left Right Top 6 1 9 4 Bottom 2 4 5 3 where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. D) What is Player 1’s maximin strategy?E) What is Player 2’s maximin strategy?F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?
5 Suppose there are only two electric vehicle producers–Tesla and BMW. Using game theory in microeconomics, explain whether BMWand Tesla willdesign the same charge plug or different plug. What factors should the firms take into consideration?
2. Consider the following game. Assume that this game is played simultaneously and without collusion. The two companies are choosing between two strategies: go international or stay national. The outcomes of each strategy for each company are given the following payoff matrix: a) Find Nash equilibrium in this game. Interpret the equilibrium you found. b) What is the Chipco's dominant strategy, if it has one? How shall Chipco's payoffs change for it to not have a dominant strategy anymore?
Suppose there are N identical firms in a market where the maximum total profit is 12. Assuming an infinite game, if the firms fully cooperate, each would get 12/N in profit. If one firm cheats, it gets the entire market profit for one period, followed by a profit of 1 in all future periods, The discount rate r is .33. How large can N be and still sustain cooperation? That is, how many firms can there be before cooperation breaks down?
Give typing answer with explanation and conclusion Suppose two firms produce identical good. The inverse demand curve for the good is: P = 240-Q, where Q is the total quantity produced by the two firms. Each firm has a constant marginal cost 20 of producing the good and fixed cost = 100. Find the Cournot Nash equilibrium of this game. What quantity will each firm produce? what will be the market price? What would be the profits of each firm?