develop and produce technology-intensive products and processes are often in a
race against competitors to become the first to achieve a certain level of technology.
These firms are faced with dilemmas in selecting the Research and Development
projects they wish to invest in and the level of investment in each one of the
selected projects. Due to the considerable uncertainty concerning the success
of different potential projects, the motivation becomes to develop resources
allocation methodologies that would yield optimal or near optimal selection and
investment decisions. We analyze the allocation problem of a firm wishing to
allocate its resources among Research and Development projects, so as to
maximize the expected discounted utility with or without budget constraint.
We consider a
model in which m possible firms compete on the completion of n possible
Research and Development projects. The model will be used to analyze aspects of
cooperative settings where a single decision-maker decides simultaneously which
projects are worthy as candidates for investment and which firms will do them
so as to maximize the total benefit for all of the firms that participate in
the Research and Development race. In contrast, we will also analyze the firms'
behavior using the Nash equilibrium solution which considers agents‘ individual
goals. Our main tool will be first order conditions and we shall explore
existence and uniqueness of the solution.