Duopoly price competition with quality improvement spillover

When competing firms embark and explore a new market, two salient features are often observed. On the one hand, the firms need to improve their quality by accumulating more experience and climbing up the learning curve. On the other hand, their quality may jointly expand the brand awareness of all competing products. In this article, we study a two-period duopoly price competition where firms can improve their quality based on the accumulated demand (learn-by-doing effect) and their potential market size is positively affected by both firms' quality levels (quality spillover effect). In addition, we investigate two pricing schemes, namely, committed pricing and dynamic pricing, and their impact on the equilibrium outcomes. Assuming the two firms are symmetric in every aspect, our main findings include the following. First, we establish the existence and uniqueness of the pure Nash equilibrium for the dynamic game under either pricing scheme, and show that firms always set a low price in the first period to leverage quality improvement. As the quality spillover effect gets stronger, firms tend to raise their first-period price, leading to a lower individual quality improvement and a non-monotonic impact on firms' profit. Moreover, we find that committed pricing scheme benefits the duopoly when the spillover effect is strong, otherwise dynamic pricing scheme brings more profits. Finally, we examine two asymmetric cases where the firms are different in certain attributes pertaining to their learning speed and the quality spillover strength. Our analysis shows that the findings in the symmetric case still hold qualitatively. Useful managerial insights are derived from these studies.