Competition in service industries

We analyze a general market for an industry of competing service facilities. Firms differentiate themselves by their price levels and the waiting time their customers experience, as well as different attributes not determined directly through competition. Our model therefore assumes that the expected demand experienced by a given firm may depend on all of the industry's price levels as well as a (steady-state) waiting-time standard, which each of the firms announces and commits itself to by proper adjustment of its capacity level. We focus primarily on a separable specification, which in addition is linear in the prices. (Alternative nonseparable or nonlinear specifications are discussed in the concluding section.) We define a firm's service level as the difference between an upper-bound benchmark for the waiting-time standard ((omega) over bar) and the firm's actual waiting-time standard. Different types of competition and the resulting equilibrium behavior may arise, depending on the industry dynamics through which the firms select their strategic choices. In one case, firms may initially select their waiting-time standards, followed by a selection of their prices in a second stage (service-level first). Alternatively, the sequence of strategic choices may be reversed (price first) or, as a third alternative, the firms may make their choices simultaneously (simultaneous competition). We model each of the service facilities as a single-server M/M/1 queueing facility, which receives a given firm-specific price for each customer served. Each firm incurs a given cost per customer served as well as cost per unit of time proportional to its adopted capacity level.