Promised delivery time and capacity games in time-based competition

We investigate firms' competitive behaviors in industries where customers are sensitive to both promised delivery time (PDT) and quality of service (QoS) measured by the on-time delivery rate. To study the competition in PDT at the marketing level, we construct an oligopoly game with an external QoS requirement. We show that there exists a unique Nash equilibrium, and the equilibrium QoS exhibits a switching surface structure with respect to capacities. To study the competition in capacity at the strategic level, we construct a two-stage game in which the firms compete in terms of their capacities in stage 1 and in terms of PDT in stage 2. We show the existence of two different types of pure strategy equilibria and characterize them. This study provides the following insights: an index of time-based competitive advantage (ITCA) and the first-mover advantage determine the positions of the firms in time-based competition; either the well-known prisoner's dilemma or off-equilibrium behaviors due to different preferences for equilibria (when multiple equilibria exist) may lead the firms to overinvest in capacity, but no one may gain a competitive advantage; a uniform improvement in internal efficiency (i. e., a uniform capacity cost reduction) may harm everyone; quality differentiation (i. e., going beyond the QoS benchmark) plays a dual role in time-based competition, either helping a firm with a larger ITCA to compete more effectively, or helping a firm possibly with a smaller ITCA to preempt competitors and protect its market advantage.