Does Firm X have a dominant strategy? If so, what is it? [ Select] Does Firm Y have a dominant strategy? If so, what is it? [Select ] Is there a Nash Equilibrium? If so, which quadrant? [ Select ]
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![Problem 3: Oligopoly Pricing
X and Y are two oligopolists who are trying to decide on how best to price their product.
Refer to the profit payoff matrix and answer the following questions. All profit figures are in
thousands.
X's possible prices
$40
$35
$57
$59
A
$60
$55
$50
$55
$69
$58
Does Firm X have a dominant strategy? If so, what is it? [Select ]
Does Firm Y have a dominant strategy? If so, what is it? [Select ]
Is there a Nash Equilibrium? If so, which quadrant? [ Select ]
Y's possible prices
$35
$40](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc777eb6c-5f00-442c-a5ae-30c50b2299ca%2F1f4baa6f-2b94-4644-acaa-71a46dd31dd1%2Fwx4kryo_processed.png&w=3840&q=75)
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- q19 If you advertise and your rival advertises, you each will earn $4 million in profits. If neither of you advertises, 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 $1 million and the non-advertising firm will earn $5 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is a. for each firm to not advertise in any year. b. for neither firm to advertise in early years but to advertise in later years. c. for each firm to advertise every year. d. for each firm to advertise in early years but not advertise in later years.QUESTION 12 This is a HOT SPOT question. You will need to evaluate the picture of the game below, and answer the question by clicking on a specific area (the hot spot) of the picture. Question: Are there any dominant strategies in this game? If there are, click on the box that corresponds to that dominant strategy (either UP, DOWN, LEFT, or RIGHT). If there aren't any anywhere outside of these boxes. If there are dominant strategies for both players, clicking on only one of them will suffice. Player 1 Player 2 Selected Coordinates Clear UP DOWN LEFT 45, 80 70, 100 RIGHT 50, 150 60, 60(KEY QUESTION) Consider the following one-shot simultaneous game (three actions for each player is the maximum we will consider in this subject, but once you get on top of this, you will see that even large games are equally easy to solve): Cindy D 6,4 5,8 6,-2 a. Before solving the game, put yourself in the position of Phil and write down your action. Then independent of that, put yourself in the position of Cindy and write down your action. b. State all the dominated strategies in the full game, by which strategy they are dominated, and 1,2 4,8 2,0 5,5 6,2 5,-1 Phil B whether weakly or strictly. c. What is the equilibrium outcome by dominance (by elimination of dominated strategies), if any? d. What are the pure strategy Nash equilibria of this game? Pick one and explain precisely (prove) why itis the Nash eguilibrium
- 1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.Dizz Cut price Maintain price Perlis Cut price (-1,-1) A (2,-2) B Maintain price (-2,2) (1,1) D Figure 12 Payoff matrix for two firms in oligopoly Two firms, Perlis and Dizz, produce washing powder in a market characterised by oligopoly. Each firm can increase its market share and profits by cutting its price relative to its rival. However if both firms cut prices they both suffer a fall in profit. This situation may be characterised as a game and Figure 12 shows the payoff matrix for this game. Figure 12 also labels each cell in the payoff matrix with a letter, A, B, C or D. Based on the information in the payoff matrix, decide which cells, if any, correspond to a Nash equilibrium. Select one answer. Select one: O There is no Nash equilibrium O D O A O A and DTwo firms are competing on a market with demand P-47-3Q by sequentially choosing how much to produce Both firms have a marginal cost of 5 In the subgame perfect Nash equilibrium: Firm 1 will produce [Select] Firm 2 will produce [Select] The equilibrium price is [Select]
- 7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Caroline are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 9 and Caroline will receive a payoff of 8. Caroline Left Right Left 8, 5 8. 7 Antonio Right 3, 6 9, 8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses and Caroline choosesWhich of the following is true for Firm 1? Peach strictly dominates Apple. Banana strictly dominates Apple. Banana strictly dominates Grapes. Grapes strictly dominates Apple. Which of the following is true for Firm 2? Blue strictly dominates Purple. Green strictly dominates Blue. Green strictly dominates Pink. Pink strictly dominates Blue. Which of the following is the IEDS (Iterated Elimination of Dominated Strategies) outcome of the game? (Apple, Pink) (Banana, Green) (Peach, Pink) (Banana, Pink) True or False: The outcome (Peach, Pink) is Pareto Efficient. True or False: (Banana, Purple) is a Nash Equilibrium.(Figure: Payoff Matrix for the United States and Canada) Use Figure: Payoff Matrix for the United States and Canada. Suppose that the United States and Canada both produce quinoa, and each country can earn more profit it output is limited and the price of quinca is high. The dominant strategy for the United States is: Canada US Low output High output Low output EU profit $10 million US profit $10 million EU profit $4 million US profit $12 million High output EU profit $12 million US profit $4 million Olow output O The United States does not have a dominant strategy O adopt a fit for tal strategy O high output EU profit $7 million US profit $7 million
- Two firms simultaneously decide whether or not to enter a market, and if yes, when to enter a market. The market lasts for 5 periods: starting in period 1 and ending in period 5. A firm that chooses to enter can enter in any of the five periods. Once a firm enters the market in any period it has to stay in the market through period 5. In any period tt that the the firm is not in the market, it earns a zero profit. In any period tt, if a firm is a monopolist in the market, it makes the profit 10t−24. In any period tt if a firm is a duopolist in the market it makes a profit of 7t−24. A firm's payoff is the total profit it earns in all the periods it is in the market. How many strategies does each firm have? Firm 1's best response to Firm 2's choice Do not enter is to enter in period: In a Nash equilibrium, Firm 1 enters in period _______ (if there is more than one answer, write any one)7. Solving for dominant strategies and the Nash equilibrium Suppose Gabriel and Nia are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Gabriel chooses Up and Nia chooses Down, Gabriel will receive a payoff of 6 and Nia will receive a payoff of 4. Gabriel Up Down Up 6,3 3,3 Nia Down 6, 4 7,4 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Gabriel chooses and Nia chooses3. Consider the following game: K Out 2 2 1 9 Player 1 Player 1 X In A Y Player 2 0 2 B 5 5 a) Does the game have perfect information? Why/why not? b) Circle the subgames. c) Find all backward induction solutions. d) Below are written five strategy profiles. One of them is a subgame perfect equilibrium; circle it! One of them is not a Nash equilibrium; write "X" across it! ((Out, X), A) ((Out, Y), A) ((In, Y),B) ((Out, Y), B) ((In, X),B)
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