In the accompanying game, firms 1 and 2 must independently decide whether to charge high or low prices. Firm 2 High Price (10,10) Low Price (5,-5) Firm 1 High Price Low Price (5,-5) (0,0) If firm 1 charges a high price when firm 2 charges a low price, then firm 2 earns
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- For the game in FIGURE 7.6, derive players’ best-reply functions, plot them as shown in Figure 7.5, and find the Nash equilibrium.Consider the following game played between an incumbent (I) a potential entrant (E): Incumbent: 80, Entrant: 40 Enter High Price Stay Out Incumbent: 120, Entrant: 0 High-Cost I, Enter Incumbent: 60, Entrant: 40 Nature Low Price Stay Out Incumbent: 100, Entrant: 0 Low-Cost Enter Incumbent: 150, Entrant: -10 Low Price Es Stay Out Incumbent: 200, Entrant: 0 Suppose the entrant observes a low price but is unsure whether they face a low-cost or high-cost incumbent, i.e. they are unsure whether they are at decision node E4 or E5. What is the maximum probability the incumbent is low cost such that the potential entrant will enter the market? Оа. 0.9 O b. 0.5 O c. 0.8 O d. 0.2Consider the following information for a static game. If you advertise and your rival advertises, you each will earn $5 million in profits. If you choose not to advertise and your rival chooses not to advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and the firm that does not advertise will earn $1 million. Assuming that each player cares only about his or her own profits, the Nash equilibrium is? Explain your answer in three long paragraphs (intro body and conclusion)
- 1. Consider the zero-sum game given by 3 1 2 A = 4 0 2 1 2 -2 3 1 (a) Calculate the gain floor and loss ceiling for A. (b) Without using dominance, use the Equilibrium Theorem to determine whether it is possible for A to have a mixed Nash Equilibrium where player two's strategy is of the form (a, b, c, 0) with a, b, c > 0.Two firms operating in the same market must decide between charging a high price or a low price. The Payoffs are as below. Firm A's profit is listed before the comma, B's profit after the comma. Firm B Firm A Low Price High Price Low Price 16, 17 7, 28 High Price 28, 7 22, 22 If each firm tries to choose a price that is optimal, regardless of the other firm's price, what is the Nash equilibrium? Does either firm have a dominant strategy?Refer to the accompanying game. Firm A Firm B Low Price High Price Low Price (10,9) (15,8) High Price (−10,7) (11,11) What are the secure strategies for firm A and firm B, respectively?
- 2- Consider the following game. Player 2 Player 1 U 12, 2 | 3, 9 5, 8 4, 2 D (a) Find all the Nash equilibria, pure and mixed. (b) Suppose that the payoff of the column player u:(D, L) is reduced from 8 to 6, but all other payoffs remain the same. Again, find all the pure- and mixed-strategy Nash equilibria. (c) Compare the mixed-strategy equilibria in parts (a) and (b). Did this worsening in one of player 2's payoffs change player 2's equilibrium mixed strategy? Did it change player l's? Give some intuition.Refer to Table Left-Right-ZigZag. How many pure strategy Nash equilibria does this game have? Table: Left-Right-ZigZag Player 1 Drive left Driver right Zigzag 1) 1 2) 2 3) 3 4) 4 5) None of the above. Drive left (1,1) (-1,-1) (0,0) Player 2 Driver right (-1,-1) (1,1) (0,0) Zigzag (0,0) (0,0) (0,0)Question 2 Suppose there are two players, an entrant and an incumbent firm playing the following game: the entrant decides whether to stay out or enter. The incumbent decides whether to innovate or not. If the entrant stays out, the entrant firm gets a payoff of 0 whereas the incumbent firm gets a payoff od 1500, independent of the action of the incumbent firm. If the entrant enters and the incumbent doesn't innovate, the entrant gets 1200 whereas the incumbent gets 500. If the entrant enters and the incumbent innovates, the entrant and the incumbent get a payoff of 1000 each. a) Draw the normal form of the game and solve for the Nash equilibrium/equilibria. b) Suppose the game is dynamic: first the entrant decides whether to enter or stay out. If the entrant enters, the incumbent decides whether to innovate or not. If the entrant stays out, the incumbent doesn't get to play. Draw the extensive form of the fame, mark the subgames on paper and solve for the subgame-perfect Nash…
- Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.4. Using a payoff matrix to determine the equilibrium outcome Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Flashfry Pricing High Low Warmbreeze Pricing High Low 11, 11 2,13 13, 2 10, 10 For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $13 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. price, and if Flashfry prices low, Warmbreeze will make more profit if it If Flashfry prices high, Warmbreeze will make more profit if it chooses a chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a chooses a price. Considering all of the…