Dropout Behavior in R&D Races with Learning
构建了一个双寡头研发竞赛博弈模型，其中研发支出和学习经验能提高发明概率。研究发现，在对称企业中，领先者从不退出，但追随者在落后太多时会退出；若企业估值或研发效率不同，领先者也可能选择退出。
We examine a game-theoretic model of a two-firm R&D race in which expenditures on R&D and the concomitant increase in experience/learning enable thefirms to increase their probability of discovering an invention. The learning process is stochastic. It generates a unique subgame-perfect equilibrium for identicalfirms with the characteristic that the leader never drops out, but the follower drops out if the leader gains a significant lead. The leader can find it optimal to drop out if the firms value the invention differently or have different R&D efficiencies. Thus, our analysis generates results between vigorous competition and natural monopoly. * Central to Schumpeter's ( 1934) vision of entrepreneurship are the extraordinary profits associated with innovation. The lure of these profits fuels the fires of creative destruction as innovators replace declining firms. This article analyzes the competition for the profits obtained by bringing an innovation to fruition and receiving the associated patent. We restrict attention to the subclass of innovations known as inventions, innovations that are the product of a firm's research and development. In particular, we are concerned with the conditions that cause a firm, after having invested in R&D, to drop out of the competitive race. Situations in which the leading firm drops out are of even greater interest. Competition in R&D is often modelled as a race in which the winner receives a patent and reaps most or all of the benefits of the invention. As exemplified by Kamien and Schwartz (1972), the early theoretical literature tended to be based on decision-theoretic models. The firm seeks an optimal rate of expenditure on R&D determined in part by the expected value of the invention, the extent of the first-mover advantage, the economies or diseconomies of scale in R&D, and the perceived intensity of rivalry. It is not anticipated that the firm's decisions will affect the R&D efforts of (the perhaps unknown) rivals. Kamien and Schwartz (1982, p. 124) show that the firm does no research if rivalry is sufficiently intense. Because their model is static, however, it is never the case that a firm enters the race and then drops out.