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 u(x.y): - x2 у +2 %3D and 16y uzx.y) = - y? 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 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 u(x.y): - x2 у +2 %3D and 16y uzx.y) = - y? 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)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question 1
![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
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Transcribed Image 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.
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