Switching queues, cultural conventions, and social welfare

We use queuing-related behavior as an instrument for assessing the social appeal of alternative cultural norms. Specifically, we study the behavior of rational and sophisticated individuals who stand in a given queue waiting to be served, and who, in order to speed up the process, consider switching to another queue. We look at two regimes that govern the possible order in which the individuals stand should they switch to the other queue: a regime in which cultural convention, social norms, and basic notions of fairness require that the order in the initial queue is preserved, and a regime without such cultural inhibitions, in which case the order in the other queue is random, with each configuration or sequence being equally likely. We seek to find out whether in these two regimes the aggregate of the behaviors of self-interested individuals adds up to the social optimum defined as the shortest possible total waiting time. To do this, we draw on a Nash Equilibrium setting. We find that in the case of the preserved order, the equilibrium outcomes are always socially optimal. However, in the case of the random order, unless the number of individuals is small, the equilibrium outcomes are not socially optimal.