Abstract
We present a stylized model of a venture capital firm being active in a specific market, where all possible projects compete. These projects have a payoff structure such that only the best few alternatives generate a positive return. The payoff depends on the relative ranking of a project’s quality in comparison with all other projects. This discontinuous payoff structure is motivated by the internet economy, where classical price competition is often not possible, and market share is chiefly determined by the relative quality ranking of the product, its absolute quality being of second order. We assume that investment alternatives show up sequentially, and, due to competition, the investment decision cannot be postponed for too long. The information available at any period is the current project’s and all prior projects’ quality characteristics. Finally, after the last investment alternative has shown up, those n projects with the highest realized quality characteristics generate positive gross returns. We derive a recursive formulation of the value function. Sufficient conditions under which the value function is non-increasing in the number of periods are provided. A simulation study demonstrates how optimal investment decisions are affected by the time horizon and by attitudes towards risk. The model presented is an extension of Bruss and Ferguson (2002).