Races of Research and Development between Firms with Different Incentives to Innovate

Summary In this paper we study a one-shot game of R & D between two firms which differ in their incentives to innovate. We analyse this problem when the R & D technology displays smoothly decreasing returns as well as when increasing returns in the form of indivisibilities prevail. In the first case we show that the magnitude of the ratio between the discount rate and the productivity of R & D expenditure may be a critical parameter in ranking firms' probabilities of winning the race. In the second case, we prove that the firm with the higher profit incentive invests in R & D at least as much as the firm with the higher competitive threat. We then apply these results to a homogeneous duopoly under Bertrand or Cournot competition in the product market.