The market (inverse) demand function for a homogeneous good is P(Q) = 10 – Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firm1 moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.
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- Consider the following Cournot game with two firms i = 1, 2. The demand function is P(Q) = 100 − Q, with Q = q1 + q2. The production costs for firm i are: C(qi) = 400 + 2qi . Find the nash equilibrium of this game. plz answer correct calculatuon asap plz dont answer by pepar1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.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 question
- Consider the Bertrand pricing game from class. If both firms have identical marginal cost of $10 and consumers will purchase from whichever firm is cheapest as long as the price is under $50, what will be the Nash equilibrium? A B C D 50, 50 50, 10 10, 10 10,50It 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 conditionsSuppose OPEC has only two producers, Saudi Arabia and Nigeria, Saudi Arabia has far more oil reserves and is the lower-cost producer compared to Nigeria. The payoff matrix in the table to the right shows the profits earned per day by each country. "Low output" corresponds to producing the OPEC assigned quota and "high output" corresponds to producing the maximum capacity beyond the assigned quota Which of the following statements is true? OA. The Nash equilibrium is a cooperative equilibrium. OB. The Nash equilibrium is a noncooperative, dominant strategy equilibrium OC. The Nash equilibrium is a collusive equilibrium. D. There is no Nash equilibrium in this game because each party. pursues its dominant strategy. Low output Nigeria High output Low output Nigeria earns $20 million Saudi Arabia Nigeria earns $30 million Saudi Arabia earns $100 million Saudi Arabia earns $80 million High output Nigeria earns $12 million Saudi Arabia earns $75 million Nigeria earns $20 million Saudi Arabia…
- The market demand function is Each firm has a marginal cost of m = $0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. The Stackelberg-Nash equilibrium quantities are The Stackelberg-Nash equilibrium price is Profits for the firms are and 92 p = $ π2 $ = Q=7,000 1,000p. 91 and units units. (Enter your responses as whole numbers.) (Enter your response rounded to two decimal places.) π₁ = $ (Enter your responses rounded to two decimal places.)Two firms, X and Y, are involved in a price war. The demand equations for each firm are the following: Qx = 52 - 2Px + Py Qy = 52 - 2Py + Px Further, assume the cost of each unit of out is constant at $4. What is the Nash equilibrium of this game? (Use the best response functions in a graph to answer) There is no Nash equilibrium O $24 $20 $2210 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 trees
- 1.7. In Section 1.2.B, we analyzed the Bertrand duopoly model with differentiated products. The case of homogeneous products. Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets. Capturesque Pricing High Low Padmania Pricing High 9, 9 3, 15 Low 15, 3 7, 7 For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $15 million, and Capturesque will earn a profit of $3 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms. If Padmania prices high, Capturesque will make more profit if it chooses a price, and if Padmania prices low, Capturesque will make more profit if it chooses a price. If Capturesque prices high, Padmania will make more profit if it chooses a price, and if Capturesque prices low, Padmania…◄ 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…