Consider a Stackelberg game played by 3 firms: firm 1 moves first, then firm 2, and finally firm 3. Inverse demand is p = 11 - Q where Q = 91 +92 +93. All firms face the same constant marginal costs c = 1. Identify the SPE of this game.
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- Consider a Cournot oligopoly with three firms i = 1, 2, 3. All firms 1. The inverse demand have the same constant marginal cost c = function of the market is given by P = 9-Q, where P is the market price, and Q =E=1 9i is the aggregate output. 13 (a) Solve for the Nash equilibrium of the game including firm out- puts, market price, aggregate output, and firm profits (Hint: the NE is symmetric). (b) Now suppose these three firms play a 2-stage game. In stage 1, they produce capacities q1, q2 and 73, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their prices p1, p2 and p3. The marginal cost for each firm to sell up to capacity is 0. It is impossible to sell more than capacity. The residual demand for firm i is 9 - Pi – Eiti; Ij if p; > p; for all j # i D; (pi, p-i) = 9-Pi 3 if pi = Pj for all j + i . if p; < p; for all j + i 9 - Pi (Note, here we assume that the efficient/parallel rationing ap-…There are two energy suppliers, Origin and Globird, and each has two possible actions: to introduce (I) or to not introduce (N) a new plan. Origin is the first firm to make a decision, and Globird is next. The extensive "tree" form of the game, and the payoffs of the two firms, are given below. Globird Origin (175,75) (25,100) Globird (50,200) (75,100) Find the subgame perfect Nash equilibria (SPNE) of this game.Refer to the normal-form game of price competition shown below. Introduce A Do Not Introduce B Clone Do Not Clone (5,5) (-10, 50) (500,0) 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 subgame perfect Nash equilibrium to this game is: Firm A plays "Do Not Introduce"; firm B plays "Clone" if firm A plays "Introduce." Firm A plays "Do Not Introduce"; firm B plays "Do Not Clone" if firm A plays "Introduce." Firm A plays "Introduce"; firm B plays "Clone" if firm A plays "Introduce." Firm A plays "Introduce"; firm B plays "Do Not Clone" if firm A plays "Introduce."
- 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.Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (p1, P2) and D2 (p1, P2) = + 2, where S > 0 and the parameter t > 0 을 + S + P2-P1 2t 2t measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms.Consider a Cournot oligopoly with three firms i = 1,2, 3. All firms have the same constant marginal cost c = 1. The inverse demand function of the market is given by P = 9-Q, where P is the market price, and Q = E1 9i is the aggregate output. 3 (a) Solve for the Nash equilibrium of the game including firm out- puts, market price, aggregate output, and firm profits (Hint: the NE is symmetric). (b) Now suppose these three firms play a 2-stage game. In stage 1, they produce capacities q1, 72 and 73, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their prices p1, p2 and p3. The marginal cost for each firm to sell up to capacity is 0. It is impossible to sell more than capacity. The residual demand for firm i is 9 – Pi - Eiti āj if pi > P; for all j # i if p; = Pj for all j # i if p; < P; for all j #i | 9-pi D; (pi, p-i) = 3 9 – p; (Note, here we assume that the efficient/parallel rationing ap-…
- (2) Consider the following two-player normal-form game: M (3,3 2,5 2,0 2, -1 1,2 Player 1/Player 2 5,1 2,2 Cu 3,60 6-3 1,4 0.0 2; 1 B 1,4 1, 1 i. Which strategy profiles survive iterated elimination of strictly dominated strategies (including pure-strategy and mixed- strategy dominances)? ii. Find all pure-strategy Nash equilibria. iii. Final all mixed-strategy Nash equilibria (excluding the ones found in part ii)).Question 1 Consider the following game. Find all Nash equilibria, subgame perfect Nash equilibria, and weak perfect Bayesian equilibria in pure and mixed strategies. a P2 (12, 12) b (12,-8) (7.-3) P1 m d (-3,2) r P2 C (2,7) d (22,17)Dennis is the International Representative of ABS-CBN and he is planning to partner with a foreign TV network, either BBC or Al-Jazeera. He also learned that ABS- CBN’s closest competitor, GMA 7, is planning to partner with a foreign TV network either CNN or Fox News. If ABS-CBN partners with BBC, it will lose $7,000 if GMA partners with CNN or gain $9000 if GMA 7 partners with Fox News. If ABS-CBN partners with Al-Jazeera, it will gain $2,000 if GMA 7 partners with CNN or lose $4,000 if GMA 7 partners with Fox News. What should be Dennis’ strategy? How much gain or loss for ABS-CBN will he expect? What should be the strategy of GMA 7?
- (a) Consider a 2-player zero-sum game with the following payoff matrix, in which a E R is some fixed value. The matrix is given, as usual, from the perspective of the row player. C1 C2 α C3 5 T1 1₂-1 2 -4 T3 2 -2 1 (i) For what range of values for a will (r₁, C₁) be a pure Nash equilibrium of this game? Justify your answer. (ii) Treating a as a constant, give a linear program to find the optimal mixed strategy for the row player. (iii) Suppose that you were given some optimal mixed strategy x for the row player. Explain how you could then determine an optimal mixed strategy y for the column player without needing to solve another linear program.Suppose that there are two firms in a market, firm 1 and firm 2. The marketis declining in size. The game starts in period 0, and the firms can compete in periods 0, 1,2, 3, ... (i.e., indefinitely) if they so choose. Duopoly profits in period t for firm 1 are equalto 105 −10t, and they are 10.5 −t for firm 2. Monopoly profits (those if a firm is the onlyone left in the market) are 510 −25t for firm 1 and 51 −2t for firm 2. At the start of eachperiod, each firm must decide either to “stay in” or “exit” if it is still active (they do sosimultaneously if both are still active). Once a firm exits, it is out of the market forever andearns zero in each period thereafter. Firms maximize their (undiscounted) sum of profits.What is this game’s subgame perfect Nash equilibrium?Company A and Company B are competing oligopolists. Both companies are considering increasing or maintaining their prices The payoff matrix shows the profits of the companies in millions based on their possible actions. Company B Increase Price Maintain Price Company A Increase Price $50, $40 $35, 530 Maintain Price 555, $45 $60, $35 The government offers a $5 milon subsidy to maintain current pricing. What is the expected outcome of the new payoff matrix, given the subsidy? The Nash equilibrium changes, and both companies will maintain their prices O The Nash equilbrium changes, and both companies will increase their prices O The Nash equilibrium remains the same, and both companies will increase their prices O Company A wit increase its price, whie Company B maintains its price. O Company A will maintain its price, while Company Bincreases ts price.