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 o
f competing firms tends to increase firms' R&D intensities, for given
beliefs, but because beliefs evolve at different rates depending on th
e 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.