Cooperation in Queueing Systems

Abstract

We study a social dilemma in a single-queue system in which human servers have discretion over the effort with which to process orders that arrive stochastically. We show theoretically that the efficient outcome in the form of high effort can be sustained in the subgame perfect equilibrium if the interactions are long term (even when each server has a short-term incentive to free ride and provide low effort). In addition, we show that queue visibility plays an important role in the type of strategies that can sustain high-effort equilibrium. In particular, we show that limiting feedback about the current state of the queue is beneficial if servers are patient enough. We conduct two controlled lab experiments to test the theoretical predictions and find that effort is increasing in the expected duration of the interaction. We also find that visibility has a strong impact on the strategies that human subjects use to provide effort in a dynamic setting. We discuss implications for managers and firms that are trying to improve service systems.

Keywords: Behavioral Operations, Single-Queue Systems, Stochastic Dynamic Games, Indefinitely Repeated Prisoner's Dilemma, Finite Mixture Models