Tragedy of the Roommates: You and your n − 1 roommates each have five hours of free time you… 1 answer below »

Tragedy of the Roommates: You and your n − 1 roommates each have five 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 c times the hours spent (individually) cleaning. That is,

Assume everyone chooses simultaneously how much time to spend cleaning.

a. Find the Nash equilibrium if c

b. Find the Nash equilibrium if c > 1.

c. Set n = 5 and c = 2. 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?