Imagine a small town with three car repair shops competing for a limited number of customers. Explain why the three shops working together to keep their prices high is unlikely to be a Nash equilibrium.
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- Two firms operating in the same market must decide between charging a high price or a low price. The Payoffs are as below. Firm A's profit is listed before the comma, B's profit after the comma. Firm B Firm A Low Price High Price Low Price 16, 17 7, 28 High Price 28, 7 22, 22 If each firm tries to choose a price that is optimal, regardless of the other firm's price, what is the Nash equilibrium? Does either firm have a dominant strategy?Jane and Sara are competing orange juice salespersons in Amherst. Their stands are next to each other on a street and consumers regard them as identical. The marginal cost of an orange juice is $1. The demand for orange juice every hour is Q = 20 − P where P is the lowest price between the two salespersons. If their prices are equal they split demand equally. a. If they set prices simultaneously (prices can be any real number), what is the Nash equilibrium price? b. If, against what we have assumed in class, orange juice salespersons have to charge prices in whole dollars ($1, $2, $3, etc), what are the Nash equilibrium prices? c. Assuming whole dollar pricing, if Jane sets her price before Sara, what price would she charge? Answer all 3 partsConsider a market organized along a 1 mile stretch of road (from D=0 to D=1). Consumers along the stretch of road are uniformly distributed. There are two firms, with Firm 1 located at mile marker .5 and Firm 2 located at mile marker 1.0 and they compete on prices. Customers choose which store to shop at according to P + cD, where c=2 and D is the distance to the store. What is the Nash Equilibrium?
- Define a dominant strategy and Nash equilibrium. Can two firms interacting with each other have no Nash equilibria if both have a dominant strategy?GAME THEORY: Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q = 40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is: A. 10 B. 15 C. 20 D. 25 E. 30QUESTION 10 Suppose there are two firms that produce an identical product. The demand curve for the product is given by P = 62 - Q where Q is the total quantity produced by the two firms. Both firms choose their individual quantities qı20 and q22 0 simultaneously. Each firm has a marginal cost of 37. What is the market price when both firms produce the quantities in the unique Nash equilibrium? Give your answer as a number to two decimal places.
- The demand for a product is Q = a - P/2. If there are 4 firms in an industry and marginal cost is MC = 20, then the price in Nash equilibrium is P = 56. What is a?Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q = 40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is 10 15 20 25 30Consider 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) 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)
- The attached diagram depicts two firms controlled by Jacob and Elsa, and two potential actions each firm might take. Payoffs from action combinations appear in the normal-form depiction of the game played by Jacob and Elsa. What is the Nash equilibrium of the game (Jacob's strategy listed first)? a b Jacob's Actions d Dont' Advertise Advertise, Advertise Advertise Don't Advertise J=300 J=400 Don't advertise, Don't advertise Elsa's Actions Don't advertise (Jacob), Advertise (Elsa) с Advertise (Jacob), Don't Advertise (Elsa) E=200 Selected answer will be automatically saved. For keyboard navigation, press up/down arrow keys to select an answer. E=50 Advertise J=100 J=200 E=300 E=100Economics Consider two firms that are choosing the price of competing products. The choices are contained in the payoff table. Each firm can raise price, lower price, or maintain their price. Suppose the game is played once each period forever. If both players play the strategy "always lower price" is this a Nash equilibrium? Let b = discount rate, 0 < b <1. Raise price Maintain price Lower price Firm B Raise price Maintain price Lower price 6. 4 8. 8 1.1 5, 5 4, 6 7.2 1.1 3.3 Firm A 2.7 No. because it is dominated by raising the price. No, because it is dominated by both firms raising the price. No, because it is dominated by maintaining the price. Yes.Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell smart phones, Flashfone and Pictech. 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 phones. Pictech Pricing High Low Flashfone Pricing High 11, 11 2, 18 Low 18, 2 10, 10 For example, the lower, left cell shows that if Flashfone prices low and Pictech prices high, Flashfone will earn a profit of $18 million and Pictech will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfone and Pictech are both profit-maximizing firms. If Flashfone prices high, Pictech will make more profit if it chooses a ______ price, and if Flashfone prices low, Pictech will make more profit if it chooses a _____ price. If Pictech prices high, Flashfone will make more profit if it chooses a _____ price, and if Pictech prices low, Flashfone will make more…
