Bounded rationality in clearing service systems

This paper considers a clearing service system where customers arrive according to a Poisson process, and decide to join the system or to balk in a boundedly rational manner. It assumes that all customers in the system are served at once when the server is available and times between consecutive services are independently and identically distributed random variables. Using logistic quantal-response functions to model bounded rationality, it first characterizes customer utility and system revenue for fixed price and degree of rationality, then solves the pricing problem of a revenue-maximizing system administrator. The analysis of the resulting expressions as functions of the degree of rationality yields several insights including: (i) for an individual customer, it is best to be perfectly rational if the price is fixed; however, when customers have the same degree of rationality and the administrator prices the service accordingly, a finite nonzero degree of rationality uniquely maximizes customer utility, (ii) system revenue grows arbitrarily large as customers tend to being irrational, (iii) social welfare is maximized when customers are perfectly rational, (iv) in all cases, at least 78% of social welfare goes to the administrator. The paper also considers a model where customers are heterogeneous with respect to their degree of rationality, explores the effect of changes in distributional parameters of the degree of rationality for fixed service price, provides a characterization for the revenue-maximizing price, and discusses the analytical difficulties arising from heterogeneity in the degree of bounded rationality.