Please try to solve it complete in 1 hour thanks Two roommates, Eric and Noah, decide independently of each other how muchtime to spend cleaning the common area of the aparment they share. Specifically, Eric chooseshe 20 (hours per week), while Noah chooses hN 2 0. They both enjoy living in a clean space,and both pay a cost for cleaning (as it leaves them less time to do other things). Their utilitywhen the apartment has been cleaned for h hours (where h = hg + hy is the total number ofhours the two roommates spend cleaning) is 20vh, while their hourly cost is a variable c>1.To summarize, their payoff functions are:u1 (he, hN) = 20Vhg +hN- chElu2(he,hN) = 20 hg + hy – chn.%3D(a)will each roommate spend cleaning?).Compute the (pure-strategy) symmetric Nash equilibrium (how many hoursSuppose Eric and Noah are getting busy with exams coming up. This increases(Б)their cost of cleaning, from c to d > c. What impact does this have on the equilibriumnumber of hours they spend cleaning?(b)Is the Nash equilibrium computed in (a) Pareto efficient? Explain.

Nash equilibrium:It is a sub-topic of game theory in which players play games and use strategy and…

Two roommates, Eric and Noah, decide independently of each other how much time to spend cleaning the common area of the aparment they share. Specifically, Eric chooses he 20 (hours per week), while Noah chooses hy 20. They both enjoy living in a clean space, and both pay a cost for cleaning (as it leaves them less time to do other things). Their utility when the apartment has been cleaned for h hours (where h = he + hy is the total number of hours the two roommates spend cleaning) is 20h, while their hourly cost is a variable c > 1. To summarize, their payoff functions are: Ju₁(he,hN) = 20√he+hN- che |u₂(he, hn) = 20√he+hN-chN. (a) Compute the (pure-strategy) symmetric Nash equilibrium (how many hours will each roommate spend cleaning?). (b) Suppose Eric and Noah are getting busy with exams coming up. This increases their cost of cleaning, from c to d > c. What impact does this have on the equilibrium number of hours they spend cleaning? Is the Nash equilibrium computed in (a) Pareto efficient? Explain. (b)

Two roommates, Eric and Noah, decide independently of each other how much time to spend cleaning the common area of the aparment they share. Specifically, Eric chooses he 20 (hours per week), while Noah chooses hy 20. They both enjoy living in a clean space, and both pay a cost for cleaning (as it leaves them less time to do other things). Their utility when the apartment has been cleaned for h hours (where h = he + hy is the total number of hours the two roommates spend cleaning) is 20h, while their hourly cost is a variable c > 1. To summarize, their payoff functions are: Ju₁(he,hN) = 20√he+hN- che |u₂(he, hn) = 20√he+hN-chN. (a) Compute the (pure-strategy) symmetric Nash equilibrium (how many hours will each roommate spend cleaning?). (b) Suppose Eric and Noah are getting busy with exams coming up. This increases their cost of cleaning, from c to d > c. What impact does this have on the equilibrium number of hours they spend cleaning? Is the Nash equilibrium computed in (a) Pareto efficient? Explain. (b)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please try to solve it complete in 1 hour thanks

Two roommates, Eric and Noah, decide independently of each other how much
time to spend cleaning the common area of the aparment they share. Specifically, Eric chooses
he 20 (hours per week), while Noah chooses hN 2 0. They both enjoy living in a clean space,
and both pay a cost for cleaning (as it leaves them less time to do other things). Their utility
when the apartment has been cleaned for h hours (where h = hg + hy is the total number of
hours the two roommates spend cleaning) is 20vh, while their hourly cost is a variable c>1.
To summarize, their payoff functions are:
u1 (he, hN) = 20Vhg +hN- chE
lu2(he,hN) = 20 hg + hy – chn.
%3D
(a)
will each roommate spend cleaning?).
Compute the (pure-strategy) symmetric Nash equilibrium (how many hours
Suppose Eric and Noah are getting busy with exams coming up. This increases
(Б)
their cost of cleaning, from c to d > c. What impact does this have on the equilibrium
number of hours they spend cleaning?
(b)
Is the Nash equilibrium computed in (a) Pareto efficient? Explain.

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Step 1: Define Nash equilibrium

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Step 2: Compute the Nash equilibrium

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Step 3: Explain the impact on equilibrium numbers

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