Scarcity of Ideas and R&D Options: Use it, Lose it, or Bank it

We investigate optimal rewards in an R&D model where substitute ideas for innovation arrive to random recipients at random times. By foregoing investment in a current idea, society as a whole preserves an option to invest in a better idea for the same market niche, but with delay. Because successive ideas may occur to different people, there is a conflict between private and social optimality. We investigate the optimal policy when the social planner learns over time about the arrival rate of ideas, and when private recipients of ideas can bank their ideas for future use. We argue that private incentives to create socially valuable options can be achieved by giving higher rewards where "ideas are scarce."