Solve for the mixed strategy Nash equilibrium of the game above. Explain carefully how you solve for it. 2. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?
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1. Solve for the mixed strategy Nash equilibrium of the game above. Explain carefully how you solve for it.
2. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?
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- Two firms A and B manufacture video game consoles. Firm A's console is less tech- nologically advanced than that of firm B, and firm A knows that if consumers get to choose between both consoles at the same time, they would choose the console of firm B. Therefore, firm A's only chance to sell a large number of consoles is to release it at a different time than firm B. Firm B prefers to release the console at the same time as firm A to benefit from the hype and blog reviews. Suppose first that the firms have to commit to a release date in advance. Firms can choose to release the console either in October or in December. Therefore, while the game has some dynamic aspect, we can think of the choice of the release date as a simultaneous move game, represented by the payoff matrix below. AB October October (10, 100) December (50, 50) December (100, 50) (10, 100) 1) What are the pure strategy Nash Equilibria of this game (if any)? Explain carefully.There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously competeTwo firms simultaneously decide whether or not to enter a market, and if yes, when to enter a market. The market lasts for 3 periods: starting in period 1 and ending in period 3. A firm that chooses to enter can enter in any of the three periods. Once a firm enters the market in any period it has to stay in the market through period 3. In any period t that the the firm is not in the market, it earns a zero profit. In any period t, if a firm is a monopolist in the market, it makes the profit 10t–24. In any period t if a firm is a duopolist in the market it makes a profit of 71-24. A firm's payoff in the game is the total profit it earns in all the periods it is in the market, or zero if it never enters the market. Is there a Nash equilibrium in which both firms enter the market?
- 1. Consider an industry with inverse demand given by p = 8 – q, where p is the price, and q is the quantity. There is one incumbent firm and one potential entrant. In the first stage of the game, the incumbent chooses its quantity qi. In the second stage, the potential entrant observes qi and chooses its quantity Ce. The potential entrant can also decide not to enter the market. The production technology of both firms are represented by the cost function C = 2q. To enter industry implies a fixed entry cost of F. (a) Find the equilibrium of the game, assuming that the potential entrant enters the industry. What are the profits of firms? (b) Assume that entry is not blockaded. For which values of F does the incumbent firm prefer to deter entry? (c) For which values of F, entry blockaded?Two organic emu ranchers, Bill and Ted, serve a small metropolitan market. Bill and Ted are Cournot competitors, making a conscious decision each year regarding how many emus to breed. The price they can charge depends on how many emus they collectively raise, and demand in this market is given by Q = 150 – P. Bill raises emus at a constant marginal and average total cost of $10; Ted raises emus at a constant marginal and average total cost of $20. Find the Cournot equilibrium price, quantity, profits, and consumer surplus. Suppose that Bill and Ted merge, and become a monopoly provider of emus. Further, suppose that Ted adopts Bill’s production techniques. Find the monopoly price, quantity, profits, and consumer surplus. Suppose that instead of merging, Bill considers buying Ted’s operation for cash. How much should Bill be willing to offer Ted to purchase his emu ranch? (Assume that the combined firms are only going to operate for one period.) Has the combination of the two…A company, say Afghan Saffron, is considering entering the Iranian’s market which is dominated by its principal rival, say Iranian Saffron. Clearly, Afghan Exporters decision to enter or not will be judged on the potential profitability of such a move. This, in turn, depends upon the way Iranian will react to such a business move by Afghan Exporters. If Iranian reacts aggressively by launching a big commercial campaign, then an entry by Afghan Saffron Exporters will result to a loss of $2.8 million for Afghan Saffron Exporters and a loss of $2.2 million for Iranian Manufacturers. If, on the other hand, Iranian accommodates Afghan Saffron exporter’s entry, then both Afghan and Iranian will be making profits of $1 million and $1 million, respectively. Finally, if Afghan Exporter does not enter the market at all, then Iranians will be making monopoly profits of $3.5 million”. Requirements: a) What would you do if you were the CEO of Afghan Saffron Exporter and Why, Explain briefly-use any…
- Two firms, A and B, are each considering trying to develop a newwidget. Whichever firm is first to develop the new widget wins a patent worth $20 million plus a penny.Developing a new widget involves several ‘steps’. The firms alternate moves, with A moving first, until oneof them wins the patent. All moves are observed. In each turn, a firm can choose whether to take 0, 1, or2 development ‘steps’. Taking 0 steps in a turn costs that firm $0. Taking 1 step in a turn costs $4 million.And taking 2 steps in a turn costs $11 million. For simplicity, assume a zero discount rate. Initially, eachfirm is 4 steps away from completing development.(a) Describe and explain carefully what will happen in this patent race and why. [Hint: it may help toread Dutta ch 12 (but notice I changed the numbers).](b) Very briefly explain what is the economic rationale for granting ‘intellectual property rights’ such aspatents. What are some disadvantages for society of granting such rights?(f) Does GaterTools have a dominant strategy? Explain using numbers from the payoff matrix.(g) Identify the Nash equilibrium. Explain why this is a Nash equilibrium using information from the payoff matrix.(h) Suppose HandyBilt makes a credible commitment to GaterTools that if GaterTools maintains its price, then HandyBiltwill pay GaterTools $250. Will this offer result in a Nash equilibrium with different strategies from those identified in part(g) ? Explain using numbers from the payoff matrix.Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here please
- 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)Macmillan Learning You notice that the prices of coffee at your local supermarket vary from week to week, causing you to buy different brands, depending on which is cheaper that week. Your friend William, by contrast, is a hardcore Peet's fan and buys only Peet's, whether the price is $5.99 per pound or $12.99 per pound. By varying coffee prices, the supermarket sells both to you, who is relatively price particular about coffee, and to William, who is relatively price and and particular about coffee. O sensitive; less; insensitive; more insensitive; more; sensitive; less sensitive; more; insensitive; less insensitive; less; sensitive; more IncorrectSave Answer Consider two cigarette companies, PM Inc. and Brown Inc. If neither company advertises, the two companies spit the market and earn $60 million each. If they both advertise, they again split the market, but profits are lower by $20 million since each company must bear the cost of advertisirlg. Yet if one company advertises while the other does not, the one that advertises attracts customers from the other. In this case, the company that advertises earns $70 million while the company that does not advertise earns only $30 million. What will these two companies do if they behave as individual profit maximizers? Neither company will advertise, and PM Inc. earns $60. One company will advertise, the other will not. Brown Inc. earns $70. Both companies will advertise, and PM Inc. earns $40. Both companies will advertise, and PM Inc. earns $60.