QUESTION 1 Consider a game in which simultaneously, player 1 selects a number x in [0,6], and player 2 selects a number y in [0,6]. The payoffs are given by 16x (x,y) = x2 y + 2 and 16у u2(x,y) = - y2...


Question 1


QUESTION 1<br>Consider a game in which simultaneously, player 1 selects a number x in [0,6], and player 2 selects a number y in [0,6]. The payoffs are given by<br>16x<br>(x,y) =<br>x2<br>y + 2<br>and<br>16у<br>u2(x,y) =<br>- y2<br>%3D<br>|<br>x +2<br>Find the unique NE of the game. Give each player's strategy as a number to 2 decimal places. Format it as follows: e.g. (5.5,7.4)<br>QUESTION 2<br>Two geographically distant firms, firm 1 and firm 2, compete in setting prices, selling the same good.<br>Suppose the consumers are uniformly distributed on the interval [0,1], and each will buy either one unit or nothing.<br>Firm 1 is located at 0 and firm 2 at 1. Firms cannot change their locations, only select prices. Firms simultaneously choose prices, firm 1 choosesp, and<br>2 chooses P2.<br>Both firms produce at zero cost and must set prices between 0 and 6.<br>Consumers care about the distance they have to travel to buy the good, but also the price. They get a benefit of 6 from the good if purchased, but als pa<br>of 2 times the distance traveled to make the purchase. If a consumer is located at x in [0.1] and they purchase from firm 1, their payoff is<br>6-2x -P1<br>Click Save and Submit to save and submit. Click Save All Answers to save all answers.<br>

Extracted text: QUESTION 1 Consider a game in which simultaneously, player 1 selects a number x in [0,6], and player 2 selects a number y in [0,6]. The payoffs are given by 16x (x,y) = x2 y + 2 and 16у u2(x,y) = - y2 %3D | x +2 Find the unique NE of the game. Give each player's strategy as a number to 2 decimal places. Format it as follows: e.g. (5.5,7.4) QUESTION 2 Two geographically distant firms, firm 1 and firm 2, compete in setting prices, selling the same good. Suppose the consumers are uniformly distributed on the interval [0,1], and each will buy either one unit or nothing. Firm 1 is located at 0 and firm 2 at 1. Firms cannot change their locations, only select prices. Firms simultaneously choose prices, firm 1 choosesp, and 2 chooses P2. Both firms produce at zero cost and must set prices between 0 and 6. Consumers care about the distance they have to travel to buy the good, but also the price. They get a benefit of 6 from the good if purchased, but als pa of 2 times the distance traveled to make the purchase. If a consumer is located at x in [0.1] and they purchase from firm 1, their payoff is 6-2x -P1 Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Jun 09, 2022
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