Optimal Dynamic Product Development and Launch for a Network of Customers

Abstract

We consider a firm that dynamically chooses its effort to develop a product for a network of customers represented by a connected graph. The technology of the product evolves as a real-valued stochastic process that depends on the firm’s dynamic efforts over time. In addition to dynamically choosing its development effort, the firm chooses when to launch or abandon the product. If the firm launches the product, the firm also chooses a selling price, a promotional price and a target customer to offer promotion. Once the target customer adopts the product, the product diffuses over the customer network based on the topology of the graph and the selling price. The product provides local network benefits to its adopters. The expected local network benefit of adoption is proportional to the number of neighbor customers that have already adopted the product. In a continuous-time setting, we explicitly solve the firm’s jointly-optimal development, launch and post-launch strategies for any connected network. We introduce metrics that allow ordering customer networks with respect to the firm’s optimal expected discounted profit, launch technology and consumer surplus. We also analyze various extensions, including multiple target customers, heterogeneity in customer demand, and heterogeneity in benefit distributions.

Keywords: optimal control, optimal stopping, dynamic product development, launch, product diffusion, graph