Allocating resources to research and development projects in a competitive environment

Firms who are involved in R&D activities are often "racing" against competitors to become the first to attain the desired breakthrough. The goal might indeed be to "beat" the competitors in as many such R&D races as possible. However, when resources are limited, and competitors' budget allocation to these R&D activities unknown, the challenge becomes to devise a method of allocating R&D budgets to activites in a strategically "optimal" way. We model the decision problem of a firm wishing to allocate a fixed budget among several activities, so as to maximize the expected profit from the activities it captures. The probability of capturing an activity is an increasing function of one's allocation to it, and a decreasing function of the competitor's allocation. For a specific plausible capture-probability function, we find the optimal allocation between two activities conditional on the competitor's allocation (the "reaction curve"). Nash and Stackelberg equilibria for that model are then characterized. We also briefly explore the implications of more general, or different, capture-probability functions.