Rachel, Monica, and Phoebe are roommates; each has 10 hours of free time you could spend cleaning your apartment. You all dislike cleaning, but you all like having a clean apartment: each person’s payoff is the total hours spent (by everyone) cleaning, minus a number 1/2 times the hours spent (individually) cleaning. That is, ui(s1, s2, s3) = s1 + s2 + s3 -1/2si Assume everyone chooses simultaneously how much time to spend cleaning. a. Find the Nash equilibrium. b. Find the Nash if the payoff for each player is: ui(s1, s2, s3) = s1 + s2 + s3 − 3si Is the Nash equilibrium Pareto efficient? If not, can you find an outcome in which everyone is better off than in the Nash equilibrium outcome?
Rachel, Monica, and Phoebe are roommates; each has 10 hours of free time you could spend cleaning your apartment. You all dislike cleaning, but you all like having a clean apartment: each person’s payoff is the total hours spent (by everyone) cleaning, minus a number 1/2 times the hours spent (individually) cleaning.
That is, ui(s1, s2, s3) = s1 + s2 + s3 -1/2si
Assume everyone chooses simultaneously how much time to spend cleaning. a. Find the Nash equilibrium. b. Find the Nash if the payoff for each player is: ui(s1, s2, s3) = s1 + s2 + s3 − 3si
Is the Nash equilibrium Pareto efficient? If not, can you find an outcome in which everyone is better off than in the Nash equilibrium outcome?
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