Dynamic R&D competition with learning

To account for the possibility that firms are unsure about the ease of innovation, we formulate a differential game of R&D competition with an unknown hazard rate. We show, as time passes without success, firms become more pessimistic about eventual innovation, reducing their R&D investment and possibly exiting the race. An increase in the number of competing firms tends to increase firms' R&D intensities, for given beliefs, but because beliefs evolve at different rates depending on the number of firms in the race, time paths of R&D investment intensity are not unambiguously ordered with respect to the number of competing firms.