The Washroom Game

This article analyses a game where players sequentially choose either to become insiders and pick one of fi nitely many locations or to remain outsiders. They will only become insiders if a minimum distance to the next player can be assured; their secondary objective is to maximise the minimal distance to other players. This is illustrated by considering the strategic behaviour of men choosing from a set of urinals in a public lavatory. However, besides very similar situations (e.g. settling of residents in a newly developed area, the selection of food patches by foraging animals, choosing seats in waiting rooms or lines in a swimming pool), the game might also relevant to the problem of placing billboards attempting to catch the attention of passers-by or similar economic situations. In the non-cooperative equilibrium, all insiders behave as if they cooperated with each other and minimised the total number of insiders. It is shown that strategic behaviour leads to an equilibrium with substantial underutilization of available locations. Increasing the number of locations tends to decrease utilization. The removal of some locations which leads to gaps can not only increase relative utilization but even absolute maximum capacity.