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Bounded Rationality in Service Networks with Open Routing

Self-interested customers populate various service systems. While self-interested, these customers may not be fully rational. We investigate the implications of boundedly rational customers on service networks where customers must visit multiple stations but can choose the order in which to visit the stations. We model customer strategy using anecdotal reasoning—that is, customers make decisions based on samples of system times experienced by customers who previously visited the system and followed each possible route. Using a fluid model, we fully characterize the evolution of customer routing decisions, with customers making decisions in each period based on anecdotal samples from the previous period. We completely specify the set of equilibrium routing profiles, where the fraction of customers choosing each route becomes stationary. In contrast with extant models of anecdotal reasoning, we find that anecdotally reasoning customers sometimes behave differently from fully rational customers, but not always. Equilibria can emerge under anecdotal reasoning that differ from fully rational equilibria, in which case, system performance suffers. Finally, we conduct extensive numerical tests, which demonstrate that our insights carry over to discrete systems that serve moderately many customers. If a service provider cannot control the service rates, then anecdotal reasoning can lead to waiting times that are much longer than necessary. However, although equilibria under customer anecdotal reasoning can differ significantly from those with fully rational customers, a service provider who controls the service rates would make the same decision under either form of customer reasoning, in both cases leading to a socially beneficial outcome.