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

Abstract

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 threshold d times the hours spent cleaning by himself. In this setting, we first determine the Nash equilibrium cleanup times when the threshold d is less than unity. Second, we find the Nash equilibrium cleanup times when the threshold d is greater than unity. Finally, for specific values of n and the threshold d , we investigate whether the second Nash equilibrium is Pareto efficient.