Service Networks With Open Routing and Procedurally Rational Customers

Self-interested customers’ form of reasoning and its consequences for system performance affect the planning decisions of service providers. We study procedurally rational customers—customers who make decisions based on a sample containing anecdotes of the system times experienced by other customers. Specifically, we consider procedurally rational customers in two-station service networks with open routing, that is, customers can choose the order in which to visit the stations. Because some actions may be less represented in the population, a given customer may not succeed in obtaining anecdotes about all possible actions. We introduce a novel sampling framework that extends the procedurally rational framework to incorporate the possibility that a customer may not receive any anecdotes for one of the actions; in this case, the customer uses a prior point estimate in lieu of the missing anecdotes. Under this framework, we study the procedurally rational equilibrium in open routing. We show first that as the sample size grows large, customers’ estimates become more accurate, and the procedurally rational equilibrium converges to the fully rational equilibrium (which is also socially optimal). We then uncover two main findings. First, we obtain bounds on the distance between the procedurally rational and fully rational equilibrium, aiding operational planning and showing the rate of convergence to the fully rational outcome as the sample size of anecdotes of each individual customer grows. Second, if customers obtain anecdotes of both actions with high probability, then the equilibrium will approximate the fully rational outcome, despite the sampling error inherent to procedural rationality.