Optimal Control Model of Software Quality for Digital Vendors

This paper models a firm's level of effort in mobile software application production as an optimal control problem to maximize market share and profit in a digital marketplace. Through a rumor-spreading system dynamic, a digital goods vendor can capture market share by focusing efforts on software quality, which is costly. We first derive theoretical results expressing market share, the state variable, in terms of effort put towards quality, the control variable. We then use numerical examples to illustrate optimal control paths for vendors facing various market conditions. Our results on effort towards quality are consistent with software evolution theory and show that focus on quality always declines over a product's life cycle. On the other hand, our findings on market share indicate that initial market conditions dictate the optimal path to pursue and affect final market share.