Firm A must decide whether or not to introduce a new product. If firm A introduces a new product, firm B must decide whether or not to clone the product. The payoff structure of the game is depicted as above. The subgame perfect Nash equilibrium to this game is: A. Firm A plays "Introduce"; firm B plays "Clone" if firm A plays "Introduce." B. Firm A plays "Do Not Introduce"; firm B plays "Clone" if firm A plays "Introduce." C. Firm A plays "Introduce"; firm B plays "Do Not Clone" if firm A plays "Introduce." D. Firm A plays "Do Not Introduce"; firm B plays "Do Not Clone" if firm A plays "Introduce."
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- q52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.14. Company A and Company B are each telecommunications manufacturers. Both companies manufacture the same products, and they make their decisions based on the other's actions. Both companies are considering opening retail outlets to increase their profits. The payoff matrix shows the profits of the companies in millions of dollars if they choose to open retail outlets. The government imposes a new $5 million tax to open retail outlets. What is the expected outcome of the new payoff matrix, given the tax? The Nash equilibrium is for Company A to not open retail outlets and for Company B to open retail outlets. The Nash equilibrium is for Company A to open retail outlets and for Company B to not open retail outlets. The Nash equilibrium is for both Company A and Company B to open retail outlets. The Nash equilibrium is for both Company A and Company B to not open retail outlets. There is no Nash equilibrium after the change given in the scenario.…16-1. Two equal sized newspaper have an overlap in circulation of 10% (10% of the subscribers subscribe to both newspaper). Advertisers are willing to pay $10 to advertise in one newspaper but only $19 to advertise in both , because they’re are unwilling to pay twice to reach the same subscribers. What’s the likely bargaining negotiation outcome if the advertisers bargain by telling each newspaper that they’re going to reach an agreement with the other newspaper so the gains to reaching agreement are only $9? Suppose the two newspaper merge. What is the likely post merger bargaining outcome?
- 16-1 Newspaper Bargaining Two equal-sized newspapers have an overlap in circulation of 10% (10% of the subscribers subscribe to both newspapers). Advertisers are willing to pay $10 to advertise in one newspaper but only $19 to advertise in both, because they’re unwilling to pay twice to reach the same subscribers. What’s the likely bargaining negotiation outcome if the advertisers bargain by telling each newspaper that they’re going to reach an agreement with the other newspaper, so the gains to reaching agreement are only $9? Suppose the two newspapers merge. What is the likely post-merger bargaining outcome? these would be most advantageous from a bargaining position?3. Describe some interaction your company has with another entity (firms producing complementary or substitute products, upstream sup- pliers, or downstream customers), or between internal divisions within your firm that can be described as a sequential or simultaneous game. Diagram the strategies, players, and compute payoffs as best you can. Compute the Nash equilibria. What can you do to change the rules of the game to your advantage? Compute the profit consequences of your advice.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?
- 7. High-tech Industry Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget: Synergy's Decision Large Budget Small Budget Dynaco's Decision Large Budget $30 million, $20 million $70 million, $0 Small Budget $0, $30 million $50 million, $40 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy a dominant strategy. If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco a dominant strategy. True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.) True False5 Consider a first-price sealed-bid auction in which bidders valuations are independently and identically distributed according to the Uniform distribution on the interval [0, 1]. Explain what the rules of the First Price Sealed bid auction are. Set it up as a Bayesian game. Compute a symmetric Bayesian Nash equilibrium for the two bidder case.1 True or False : Every finite extensive - form game of imperfect information admits at least one pure - strategy Nash equilibrium . Justify if true or give a counter - example if not
- Exercise 3: merger example Algoma Steel Inc. and Stelco Steel Inc. Merger? Suppose you work at the Bureau and your task is to assess a proposed merger between Algoma Steel Inc. and Stelco Steel Inc. For simplicity, these are the only two firms in Canada. The cost of this merger is that the two firms will become one joint firm, or the duopolists become the monopolist. This is likely to limit consumer choices and the equilibrium price is likely to rise. However, this merger is likely to increase economies of scale, or production cost will fall. From existing studies you know the following information, and P is the price per ton of steel and Q is the number of tons of steel. Demand for steel: P = 1,800 - Q Marginal revenue: MR = 1,800 - 2Q Supply of steel: MC = ATC = 600, identical across the two firms. Case #1: Before Merger - Cournot duopoly - the government does not intervene The total surplus (TS), defined as the sum of consumer surplus and producer surplus, is equal to…10) Consider a repeated game in which the following one-shot game between two players is repeated "infinitely." Denote by "d" the discount factor. (Assume both players have the same discount factor.) Player 2 Cooperate Defect Player 1 Cooperate 5, 4 0, 5 Defect 6, 0 1, 1 The two players try to support cooperation by using "grim trigger strategy" as discussed in class. Answer YES or NO to each of the following three questions. (a) Can they support cooperation if the common discount factor, d, is equal to 0.23? (b) Can they support cooperation if the common discount factor, d, is equal to 0.4? (c) Can they support cooperation if the common discount factor, d, is equal to 0.15?4. Consider the following Stackelberg game. Firm 1, the leader, selects an output,q1, after which firm 2, the follower, observes the choice of q1, and selects its own output, q2. The resulting price is one satisfying the industry demand curve P=200-q1-q2 . Both firms have a constant marginal cost of 60. a. Derive the equation for the follower firm’s best response function. b. Determine the equilibrium output and price of the Stackelberg game. What are the profits for the leader and follower firm in the equilibrium?