QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P1, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2(P1, P2) 140 - 2p2 + P₁ Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)
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- Problem 3. Consider the following game with three firms. First, firms 1 and 2 si- multancously choose quantities q1 and q2 respectively. After observing firm 1 and 2's quantities, firm 3 chooses its quantity q3. There is no production cost and the inverse demand function is p= 12 – (91 +2 + 93). (a) Compute the SPNE of this game. (b) Give an example of Nash equilibrium s* with s = 4 and s, = 6 , that is not subgame perfect. game theory questionConsider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)◄ Search 12:47 PM Sun Nov 12 ← Note Nov 12, 2023 Uptown's price strategy The Nash equilibrium occurs when High Low LED RareAir's price strategy High $12 $15 The more favorable outcome would be for $12 Tt ✪ $6 B Low $6 D $8. $15 $8 S O both firms have an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell A. 92% neither firm has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the dominant strategy of cell D. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell B. O one firm consistently has an incentive to deviate from this strategy given the strategy of the competing firm. It is shown by the high-price strategy of cell C. O the firms to collude and use the high-price strategy but this strategy requires cooperation. O one firm to take the lead and let the…
- Which one of following statements is false? * Consider the following game. B D E F There are 7 subgames in this extensive-form game. There are 6 proper subgames in this extensive-form game. (BK, CE) is a Subgame Perfect Nash Equilibrium. O (BK, DE) is a Subgame Perfect Nash Equilibrium. G H I J K L M N 3,4 4,3 1,2 -5,7 6,5 2,8 9,1 3,62. Provide the normal-form expression to the extensive-form game below, and find all pure-strategy Nash equilibria there. Find the subgame-perfect Nash equilibrium then. A B X E Y B A B F t G F G BF B D A 0 3. Find the subgame perfect Nash equilibria (may or may not be unique) in the game below. A B 100 30 F 60 9 5 B 3 5 12 10 60 10 80 10 180 60 200 40Consider the game R T 11 1.0 10 M 014.0 0.1 B 0.10. 4.0 (a) Find the Nash equilibrium in pure strategies. (b) Find the Nash equilibrium in completely mixed strategies. (c) Find the Nash equilibrium in partially mixed strategies ove the support {A. B} x {C.R).
- 10 logging firms use a forest to collect timber. Each firm i must choose how many trees to cut, gj The benefit of cutting a tree is 1000 -2G per tree, where G is the total quantity of trees cut in the forest. The marginal cost of cutting a tree is 10G. Firms do not face any fixed costs. In a Nash Equilibrium, O Each firm cuts 125 trees O Each firm cuts 125/10 trees O Each firm cuts 125/4 trees O Each firm cuts 5 trees6. Consider two ice cream sellers competing at a beach that is 1000 metres long. Ice cream prices are fixed by the ice cream company, but companies can choose their locations simultaneously. Customers are located uniformly (spread out evenly on the beach) and do not like walking. The cost of walking every metre is the same (i.e. linear cost). a) Where will the ice cream stands be located in the Nash equilibrium if the locations are chosen simultaneously? b) What are the socially optimal locations, i.e. the best from society’s point of view that minimise transportation cost? Are the locations in the Nash equilibrium different from the socially optimal locations? Explain. c) Suppose there are three ice cream sellers that locate simultaneously. Find the Nash equilibrium is there is one. Else, explain why there is none. (Focus on pure strategy Nash equilibria)It takes 3,000 households having average annual income of $50,000 within a 3-mile radius to support a grocerystore. There are actually 6,000 households within 3-miles of the Shop-Rite Grocery that have $50,000 per yearaverage incomes. Today, Shop-Rite is the only grocery store in this area. Using the concept of Nash Equilibrium inlocation, explain what the likely outcome will be for this area, given those conditions
- 6. Consider two ice cream sellers competing at a beach that is 1000 metres long. Ice cream prices are fixed by the ice cream company, but companies can choose their locations simultaneously. Customers are located uniformly (spread out evenly on the beach) and do not like walking. The cost of walking every metre is the same (i.e. linear cost). Where will the ice cream stands be located in the Nash equilibrium if the locations are chosen simultaneously? а. b. What are the socially optimal locations, i.e. the best from society's point of view that minimise transportation cost? Are the locations in the Nash equilibrium different from the socially optimal locations? Explain. Suppose there are three ice cream sellers that locate simultaneously. Find the Nash equilibrium is there is one. Else, explain why there is none. (Focus on pure strategy Nash equilibria) С.The following information regarding the outcome of choices between two firms is provided as follows: Firm 2 Strategy A B A 20, 40 30, 16 B -20, 14 20, 20 Firm 1 Does firm 2 have a dominant strategy? What is the secure strategy for firm 2? What are the Nash equilibrium strategies for firms 1 and 2?Pay-offs (in terms of profit) for the two firms are give Firm2 startegies Firm1 Strategies C B W C [4, 4] [0, 5] [-1, 5] [5, 0] [2, 2] [-1, 1] W [5, -1] [1, -1] [0, 0] a)What is a dominant strategy for each player? b)What are the possible pure strategy Nash equilibrium/equilibria to the one-shot play of this game? c) Explain the likely out the game