Extensive Form, Multistage Game: Firm A currently monopolizes its market and earns profits of $10M. Firm B is a potential entrant that is thinking about entering the market. If B does not enter the market,it earns profits of $0, while A continues to earn profits of $10M. If B enters, then A must choose between accommodating entry and fighting it. If A accommodates, the A earns $5M and B earns $5M. If Afights, both lose $5M. Draw the game in extensive form and predict the outcome.Again, EXTEND the above game. Now, suppose the decision of B to enter is reversible in the following way. After B enters the market, and A has decided to either fight or accommodate, B can choose to remain inthe market or exit. All payoffs from the above game remain the same. However, if B decides to exit the market, then B suffers a loss of $1 M, while A regains the old profit of $10M. Draw the game in extensive formand predict the outcome.

To determine the sequential optimum action of players (firm A and B) the backward induction method…

Answered: Extensive Form, Multistage Game: Firm A…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.7P

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Firm A Firm B Low Price High Price Low Price (2, 2) (10, −8) High Price (−8, 10) (15, 15) Suppose the game is infinitely repeated, and the interest rate is 10 percent. The firms are allowed to collude and make joint decisions. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats (by charging a low price), then the agreement is no longer valid and each firm may make their own independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.
Olivia is thinking about opening a new bakery (the entrant). There is already a bakery open in her neighborhood (the incumbent), and the owner of the incumbent bakery makes it clear that if Olivia enters the market, they will cut their prices in an attempt to drive the new bakery out of business. Based on the payoff matrix below, is the incumbent’s threat credible? That is, if Olivia opens a new bakery, will the incumbent actually lower their prices? Note: the entrant chooses the row, the incumbent chooses the column High price Low price Enter 1, 2 -1, 1 Don’t enter 0, 10 0, 1 a. Yes, the threat is credible b. No, the threat is not credible
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.
Suppose that two firms, firm A and firm B, are competing in the market. Assume that each firm has two strategies available: “no promotion” and “extensive promotion”. If both firms choose “no promotion”, each firm will get a payoff of 8000. If both firms choose “extensive promotion”, each firm will get a payoff of 5000. If one firm chooses “no promotion” and the other firm chooses “extensive promotion”, the firm that chooses “no promotion” will get a payoff of 4000 and the firm that chooses “extensive promotion” will get a payoff of 10000.a. Assume the game is a 2-players one-shot simultaneous game, please develop the normal form of this game by showing the players, the strategies and the payoffs. b. Follow part (a), determine the dominant strategy of firm A. c. Follow part (a), determine the dominant strategy of firm B. d. Follow part (a), determine the equilibrium of this game. e. If the game becomes an infinitely repeated game, what do you expect to happen?
Two firms, Firm 1 and Firm 2 are considering simultaneously developing a new product for a market. The costs of developing the product are $5m and there will be a total revenue in the market of only $60m if only one of the firms develops the product. If both firms do not develop the product then there will be a total of $90m available in revenue from the market and Firm 1 will receive 60% of the market share and Firm 2 will receive 40% of the market share. a) Capture this entry game in a payoff matrix b) What is the Nash equilibrium c) Does either firm have a dominant strategy? plz answer me as soon as possible
Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).
Two firms are competing to establish one of two new wireless communication standards, A or B. A strategy is a choice of standard, and an outcome of this game is a choice of standard by each firm – for example, (A, B) represents the case where Firm 1 decides to develop standard A and Firm 2 develops standard B. Here, the first letter will always correspond to Firm 1’s decision, and the second letter to Firm 2’s decision. Firm 1 has the following preferences over outcomes, in order of highest to lowest preferred: it prefers (A, A) to (B, A) to (A, B) to (B, B). Firm 2 prefers (A, B) to (A, A) to (B, A) to (B, B). Suppose that firms simultaneously decide which standard to develop. What is the pure strategy Nash equilibrium? Is the answer (B,B)? If not please explian what is the answer?
Consider the following entry-deterrence game. A potential entrant has two strategies, “Enter” or “Stay Out”. An incumbent firm can either Price Low or Price High, depending on whether they want to try to fight or accommodate the entrant. (The Price Low option could be a limit price, for example). Suppose if the entrant Enters and the incumbent Prices Low, both firms lose $-1M. If the entrant enters and the incumbent Prices High, each firm earns $2M. If the Entrant doesn’t enter, the incumbent earns $4M and the entrant earns $0. a)Using the concept of Nash Equilibrium, what are the predicted strategies and profits? Set up a game box or tree and explain your reasoning. b) Give an example of a different profit outcome that would lead to a different Nash Equilibrium. (From this, you can see that sometimes deterrence is effective and sometimes it isn’t, depending on the profits).
Table 17-6 Two home - improvement stores (Lopes and HomeMax) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. The following game depicts the strategic outcomes that result from the game. Increases in annual profits (in millions of dollars) of the two home - improvement stores are shown in the following figure. Refer to Table 17-6. Increasing the size of its store and parking lot is a dominant strategy for Question 8 options: Lopes, but not for HomeMax. HomeMax, but not for Lopes. both stores. neither store.
Sometimes oligopolies in the same industry are very different in size. Suppose we have a duopoly where one firm(Firm A) is large and the other firm (Firm B) is small, as the prisoner’s dilemma box in Table 10.4 shows. Assuming that both firms know the payoffs, what is the likely outcome in this case?
4. Firm 1 and firm 2 are car producers. Each has the option of producing either a big car or a small car. The payoffs to each of the four possible combinations are given in the following payoff matrix. Each firm must make its choice without knowing what the other has chosen. The first number in each cell refers to the payoffs for Firm 2. FIRM 2 Big Car Small Car COMPANY ABC FIRM 1 Low Price Big Car 400, 400 High Price 800, 1000 a. Does either firm have a dominant strategy in this case? Explain your answer clearly. b. Identify all Nash equilibria for this game. Suppose there are 2 players in a non-cooperative game theory situation. Company ABC and Company JKL both sell books and can choose to charge a high price or a low price for a particular book that is very popular. The following matrix contains the payoffs that each company receives under 4 scenarios. The first number in each cell refers to the payoffs for Company ABC. COMPANY JKL Small Car Low Price 1000, 800 200, 300 100, 600…
The following payoff table lists the profits of a buyer and a seller. The seller acts first by choosing a sale price ($9, $8, or $6). The buyer then decides the quantity of the good to purchase (two units, four units, six units, or eight units). a. Suppose the buyer and seller transact only once. Does the buyer have a dominant strategy? Depending on the price quoted, what is his best response? What price should the seller set? Explain carefully. Buyer Quantities 2 Units 4 Units 6 Units 8 Units P $9 10, 6 20, 5 30, 0 40, 8 Seller P $8 8, 8 16, 9 24, 6 32, 0 Prices P $6 4, 12 8, 17 12, 18 16, 16 b. Suppose the seller and buyer are in a multiyear relationship. Each month, the buyer quotes a price and the seller selects her quantity. How might this change each player’s behavior? c. Now suppose the buyer and seller are in a position to negotiate an agreement specifying price and quantity. Can they improve on the result in part (a)? Which quantity should they set? What price would be…

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