Price competition of make-to-order firms

In recent years, there has been considerable research on price competition in a market where customers are sensitive to production or service delays. Most of these works assume identical firms with only different service speeds (capacities), and find that the firm with the higher speed can usually charge a premium price and take a larger market share. We consider the (non-cooperative) competition of two make-to-order firms. In addition to different service capacities, the competing firms may provide different values of service, and have firm-dependent unit costs of waiting. We obtain sufficient conditions for the existence of a Nash equilibrium, and we characterize the equilibrium analytically for some cases and numerically for some other cases. Our results confirm that the firm with the higher speed of service can usually charge a premium price and does take a larger market share. In addition, we find that the firm with the higher value of service and lower cost of waiting can usually charge a premium price and also take a larger market share. However, we do find cases where the faster (while otherwise identical) firm may charge a lower price, or take a smaller market share, or even generate less profit. In response to an increase in its service capacity, a firm may either raise or cut its optimal price, even though a higher service capacity always leads to a shorter expected waiting time. The firm may either raise or cut its price in response to a hike in its unit waiting cost.