Optimal Apartment Cleaning by Harried College Students : A Game-Theoretic Analysis

In this note we use a simple game model to analyze the optimal cleanup of an apartment that is shared by n ∈ ℕ college students who are pressed for time. From an individual standpoint, these students dislike cleaning. However, they also prefer a clean apartment to a dirty one. Hence, for any student i, where i=1,...,n, this student's utility is the total number of hours spent by all the n students cleaning less a number d times the hours spent cleaning by himself. In this setting, we first determine the Nash equilibrium cleanup times when the number d is less than unity. Second, we find the Nash equilibrium cleanup times when d is greater than unity. Finally, for specific values of n and d, we investigate whether the second Nash equilibrium is Pareto efficient