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- 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…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 False1. 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?
- (Table: Samsung and Apple’s Payoff Table) Suppose that a market is dominated by two large firms, Samsung and Apple. Both have two choices: to Advertise or Do not advertise. The payoff table below shows the potential revenues associated with each firm’s strategies. For example, if Apple advertises and Samsung does not, the payoff to Apple is $75,000 and Samsung’s payoff is -$25,000. What are Apple and Samsung’s respective dominant strategies? Apple (right payoffs) Samsung Do not advertise Advertise Do not advertise (50000, 50000) (-25000, 75000) Advertise (75000, -25,000) (10000,10000) Group of answer choices Do not advertise, Do not advertise Advertise, Advertise Do not Advertise, Advertise Advertise, Do not Advertise10) 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?6 Two people will select a policy that affects both of them by applying a "veto" in a sequential and alternate manner, that is: person 1 begins to veto a policy and then person 2 exercises his "veto" with the remaining policies; the process repeats until only one policy remains. Assume that there are 3 policies: X,Y,Z, and that person 1 prefers X to Y to Z and person 2 prefers Z to Y to X. a. Represents the game extensively b. Give the number of subgames C. Indicate the total strategies of the players d. find all subgame perfect nash equilibria e. Find all Nash Equilibriums.
- 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?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?
- 10. Game theory terminology Select the term that best describes each definition listed in the following table. Definition Nash Equilibrium Dominant Strategy Collusion Tit-for-tat Strategy Payoff Matrix/Table Prisoners' Dilemma Game A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again A case in which individually rational behaviour leads to a jointly inefficient outcome A player's best choice, if it exists, regardless of his or her opponent's strategypractice 9 [LEARN-APPLY] A Firm Entry Game with Sequential Moves, Drawing Game Tree, Finding Rollbak Equilibrium / Subgame Perfect Equilibrium S4. Consider the rivalry between Firm A and Firm B to develop a new commercial jet aircraft. Suppose Firm B is ahead in the development process and Firm A is considering whether to enter the competition. - If Firm A stays out, it earns zero profit, whereas Firm B enjoys a monopoly and earns a profit of $1000 million. - If Firm A decides to enter and develop the rival airplane, then Firm B has to decide whether to accommodate Firm A peaceably or to fight by starting a price war. In the event of peaceful competition, each firm will make a profit of $300 million. If there is a price war, each will lose $100 million because the prices of airplanes will fall so low that neither firm will be able to recoup its development costs. Source: Chapter 3, Games of Strategy, by Avinash Dixit, Susan Skeath, David H. Reiley, 3rd edition, W.W. Norton &…33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.
