For the following pay off matrix of firm A, determine the optimal strategies for both the firms and the value of the game: Firm B B, B2 Ba BA B5 A, 3 -1 6 Firm A A2 -1 8. 4 12 Ag 16 6 14 12 A4 1 11 -4 1
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- 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.…Economics - Game Theory & Business Strategy Inverse Market Demand for tires is P = 200 - .01Q We assume the manufacturer sets a Price, 'X', for the tires and the manufacrturer moves first, selecting 'X' before any sales decisions are made. In this variation, we assume there are 3 retail firms, each with Market Power. The firms (1,2,3) make their sales decisions (q1,q2,q3) simultaneously, taking the manufacturer's price X as given. Total market sales, Q, then equal q1 + q2 + q3. We assume the only cost for the retailers is the cost 'X' for each tire. Additionally, the manufacturer produces the tires at a Marginal Cost of $10 a tire. **** Write out the Extensive form of this game ****For questions 32 - 35 consider the following "research and development" game. Firms A and B are contemplating whether or not to invest in R8D. Each has two options: "Invest" and "Abstain." A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn't invent X. it makes 50 in revenue. If a firm invests and is the only one to invent X. it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other's investment decisions. Find the Nash Equilibrium (or Equilibria) of the "research and development" game. A. There are no Nash Equilibria B. Invest/Invest C. Invest/Abstain, and…
- For questions 32 - 35 consider the following "research and development" game. Firms A and B are contemplating whether or not to invest in R8D. Each has two options: "Invest" and "Abstain." A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn't invent X. it makes 50 in revenue. If a firm invests and is the only one to invent X. it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other's investment decisions. Find the Nash Equilibrium (or Equilibria) of the "research and development" game. There are no Nash Equilibria Invest/Invest Invest/Abstain, and Abstain/Invests…1 \ 2 a b c A 2,2 2,1 0,0 B 3,1 3,0 1,3 C 1,3 3,2 3,1 a) Eliminate iteratively all strictly dominated strategies. b) Find all Nash equilibria. c) What is the player 1’s best response to the strategy σ2 = (z , ½ , ½ - z) of player 2, where z is a parameter that lies in the closed interval [0, ½]. d) Compute the payoffs to player 1 and to player 2 for their respective strategy profiles σ1 = (0,½,½) and σ2 = (½,0,½).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?
- This activity has 4 theorical and practical exercises for which you will have to describe the representation of each proposed game and its solutions.1. Consider the following game in strategic or normal form.A2 B2 C2A1 1,0 1,2 -2,1B1 6,2 0,3 2,3C1 2,2 -2,1 2,3▸ Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible.▸ What is the set of rationalizable strategies for each player? Microeconomics (code ECO2023)Actividades 2© MIU City University Miami ▸ What is/are Nash equilibrium(s) in this game?▸ Explain the differences between cooperative and non- cooperative games. What are the fundamental hypotheses about the behavior of the persons in Game theory?2. Two hunters may choose, individually and simultaneously, to go deer hunting, as the deer can provide abundant and appetizing food, or to go hare hunting, also appetizing, but scarce. Deer hunting represents a challenge and requires mutual coordination. Hunting a…Consider a bankruptcy game with two risk-neutral players where V = $600,000, C1 = $400,000, and C2 = $800,000. What is the Nash bargaining solution?The value of x is 0<x<90. For what value of x is (D, R) a risk dominant equilibrium. Game Bob L RAnn U 100,100 0, 0 D x, x 90, 90 Select one: a.none of the other answers. b.It is never risk dominant. c.For all x, where 0<x<50 d.For all x, 0<x<90. e.It is always risk dominant
- 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?Consider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000 a) What is the Kalai-Smorodinsky bargaining solution?Analyze the pure Nash equilibrium and mixed Nash equilibrium strategies in the following manufacturer–distributor coordination game. How would you recommend restructuring the game to secure higher expected profit for the manufacturer?