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Suppose firm A and firm B repeatedly face the situation presented in Table and the interest rate is 40 percent. The firms agree to charge a high
![Table 10-7
A Pricing Game That Is Repeated
Firm B
Price
Low
High
Low
0,0
50, –40
Firm A
High
-40, 50
10, 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd4cd64-ecd7-4ba0-887c-578da2c6cd10%2F67ae18e8-6ea4-4e65-8c15-785a183cc30e%2F8dwbgu.jpeg&w=3840&q=75)
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- 1. Two firms compete in price in a market for infinite periods. In this market, there are N consumers; each buys one unit per period if the price does not exceed $10 and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume N/2 consumers buy from each firm. Assume zero production cost for both firms. A possible strategy that may support the collusive equilibrium is: Announce a price of $10 if the equilibrium price has always been $10; otherwise, announce the price as in Nash equilibrium of the one-shot Bertrand game. 1.a Let & be the discount factor. Find the condition on & such that the above strategy can indeed support the collusive equilibrium. Now suppose that Firm 2's marginal cost is $4, but Firm 1's marginal cost remains at zero. 1.b Find the condition on & under which Firm 2 will not deviate from the collusive equilibrium. 1.c Find the condition on under which Firm 1 will not deviate from the collusive…1. Two firms compete in price in a market for infinite periods. In this market, there are N consumers; each buys one unit per period if the price does not exceed $10 and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume N/2 consumers buy from each firm. Assume zero production cost for both firms. A possible strategy that may support the collusive equilibrium is: Announce a price of $10 if the equilibrium price has always been $10; otherwise, announce the price as in Nash equilibrium of the one-shot Bertrand game.HP and Sony compete primarily by price. Each firm must choose either a high price or a low price simultaneously. Use the following information to create the profit matrix: If HP and Lenovo both set high prices, HP’s profit is $40 million and Sony’s profit is $35 million. If HP sets high price and Sony sets low price, HP’s profit is $25 million and Sony’s profit is $40 million. If HP sets low price and Sony sets high price, HP’s profit is $50 million and Sony’s profit is $10 million. If HP and Sony set low prices, HP has $20 million and Sony has $15 million. Please answer the follow questions: Does Sony have a dominant strategy? HP? If so, which one? If HP and Sony maximize their profits non-cooperatively, what is the Nash-equilibrium for this profit matrix? Instead, if HP and Sony maximize their joint profits cooperatively, what is the equilibrium? Assume they keep their agreements.
- 4. Two Stackelberg-competitors with no costs face the common market demand curve P=30−Q, where Q is the combined output of both firms. Firm 1, the leader, picks its output first. Then Firm 2, the follower, picks its output. How much output does Firm 2 produce in their sequential-move game? a) 3 units. b) 15 units. c) 15/2 units. d) 30 units.2. Consider the following "location game." There are two ice cream sellers (Seller 1 and Seller 2) in a small city. Residents are uniformly located on a straight street of length 1. The ice cream sellers need to choose where to set up their carts, and each resident will purchase one unit of ice cream from the nearest seller. The city council has fixed the price of the ice cream, and as a result, each seller just wants sell as much ice cream as possible. (a) We think of this "location game" as a simultaneous-move game, in which each player's payoff is the proportion of residents that buy from her cart. Is this game with discrete strategies or continuous strategies? Please state the set of (pure) strategies for both sellers. Is this game zero-sum or non-zero-sum? (b) Find all NE(s) of this game. (c) Is there an alternative pair of locations for the sellers such that the residents’ total walking distance is reduced but neither seller is hurt? Is it an NE? (d) Suppose now that there are…Using a payoff matrix/table to determine the equilibrium outcome Suppose there are only two firms that sell smartphones, Flashfone and Pictech. The following payoff matrix/table shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its phones. Pictech Pricing High Low Flashfone Pricing High 10, 10 4, 12 Low 12, 4 9, 9 For example, the lower left cell shows that if Flashfone prices low and Pictech prices high, Flashfone will earn a profit of $12 million and Pictech will earn a profit of $4 million. Assume this is a simultaneous game and that Flashfone and Pictech are both profit-maximizing firms. If Flashfone prices high, Pictech will make more profit if it chooses a price, and if Flashfone prices low, Pictech will make more profit if it chooses a price. If Pictech prices high, Flashfone will make more profit if it chooses a price, and if Pictech prices low, Flashfone will make…
- Let ci be the constant marginal and average cost for firm i (so that firms may have different marginal costs). Suppose demand is given by P=1-Q. Calculate the Nash equilibrium quantities assuming there are two firms in a Cournot market. Also compute market output, market price, firm profits, industry prof- its, consumer surplus, and total welfare. Represent the Nash equilibrium on a best-response function diagram. Show how a reduction in firm 1’s cost would change the equilibrium. Draw a representative isoprofit for firm 1.Question 3 Assume we have a market with only two companies in it, Company X and Company Y. Now suppose that both companies have to choose one of two potential strategies for pricing their products: setting a low price or setting a high price. The table below shows the expected profits for each company under each pricing scenario. Assume both companies are in competition with each other and seek to maximize their profits. Under these conditions, how much profit should we expect both companies to earn? Company Y Provide your answer below: High Price Low Price High Price Profit for Company Y: $12, 975,000 Profit for Company X: $12, 975,000 Profit for Company Y: $16, 218,000 Profit for Company X: $1,946, 000 Company X Low Price Profit for Company Y: $1,946, 000 Profit for Company X: $16, 218,000 Profit for Company Y: $6,487,000 Profit for Company X: $6,487,000Consider the following game. Firm 1, the leader, selects an output ?1, after which firm 2, the follower, observes the choice of ?1 and then selects its own output ?2. The resulting price is one satisfying the industry demand curve ? = 200 − ?. Both firms have zero fixed costs and a constant marginal cost of 60. Determine the equilibrium output of each firm in the leader-follower game. What are firm 1’s profits in the equilibrium?
- Suppose that two clothing manufacturers, Lands’ End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands’ Ends Profit, LL Bean’s Profit) is attached in the payoff matrix below: a.) What is the Nash equilibrium and expected profits to LL Bean and Lands’ End of this game? b.) Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a priceof $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a1/3 chance of choosing each strategy. What’s the expected payoff to LL Bean? c.) Suppose that in hopes of raising…The payoff matrix in the figure to the right shows the payoffs for a pricing game. If you were firm A, which strategy would you choose? Firm A should A. price high because this is their maximin strategy. B. price low because this is their tit-for-tat strategy. C. price high because this is their dominant strategy. D. price low because this is their dominant strategy. E. price low because this maximizes profits of both firms. Firm B's dominant strategy is to price If this game were repeated a large number of times and you were firm A and you could change your strategy, what might you do? Firm A should O A. use a tit-for-tat strategy by responding in kind to firm B's play. B. use a maximin strategy by maximizing the minimum gain that can be earned. C. use a tit-for-tat strategy by selecting a price that minimizes firm B's profits. D. use a maximin strategy by by responding in kind to firm B's play. E. use a tit-for-tat strategy by maximizing the minimum gain that can be earned. C Price…Consider the payoff matrix below representing two firms engaged in Bertrand Competition. Firm A is player 1 and Firm B is player 2. High price Low price High price 10, 12 -1, 13 Low price 12, 2 0, 3 What is Firm A's dominant strategy? Question 14Answer a. High price b. Low price c. Firm A does not have a dominant strategy
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