تجربه تولید و ساختار بازار در رقابت تحقیق و توسعه

In the R&D race the incumbent enjoys an advantage of learning from production experiences, but this important feature has not been incorporated into existing studies. Assuming that the technological knowledge is accumulated not only by R&D expenditures but also by production experiences, we study the properties of optimal investment strategies in a model with an incumbent and many identical challengers. After proving the existence of a unique Nash equilibrium in the R&D race, we demonstrate analytically that the likelihood of persistent leadership increases with production experiences of the incumbent but decreases with the number of challengers. Numerical analyses also establish that (i) the challengers always invest more than the incumbent and the difference increases with production experiences, the flow of monopoly profits and the number of challengers; and (ii) the likelihood of persistent leadership increases with the value of being the winner and the value of being a loser but decreases with expected waiting time of R&D innovation and the flow of monopoly profits. However, destructive innovations may still occur even when production experiences are allowed to play an important role in the R&D competition.

In this paper we develop a framework to understand the impact of production experiences on the R&D race and study whether the incumbent can prevail in the face of possibly destructive innovations. Although the effects of production experiences on production costs1 and the structure of an industry2 are in the literature, their impact on the R&D race has not been fully analyzed. Production experiences can play to the advantages of the incumbent in the R&D competition. For example, Intel's experience of producing 486 CPU provided the company with an opportunity to supersede its major rivals in the development of the products of the next four generations – namely, Pentium I, Pentium II, Pentium III, and Pentium IV CPUs (Yu, 1999 and Chang and Park, 2004). Similarly, Gruber's (1994) empirical studies also show that production experiences helped the incumbent to prevail in the patent race for the next-generation EPROMs products. Production experiences, however, may not be sufficient for the incumbent to sustain its edge over its competitors as more challengers emerge. In the optical passive components (OPC) industry for example, an increase of new competitors from Taiwan and Korea caused most of the Japanese and American incumbents to switch to the optical active components (OAC) industry. It shows that destructive innovations may occur as the R&D race becomes more competitive. In a seminal paper, Reinganum (1982) studies the strategies of a number of identical firms engaged in R&D race. An increase in the number of challengers is shown to lead to an increase in each firm's R&D investment.3Reinganum (1983) also points out that the incumbent's R&D investment is less than that of the challenger when there is only one challenger and one incumbent and when the innovation process is uncertain. Furthermore, when there is one incumbent and a number of identical challengers and when the new-generation products are introduced to replace the obsolete products as in Reinganum (1985), the incumbent always invests less than the challengers since the incumbent lacks an incentive for R&D investments. Hence, the Schumpeterian ‘process of destructive innovations’ can occur in a sequence of innovations as the incumbent is overthrown by a more innovative challenger.4 In this paper, we include not only the impact of market competition but also the effects of accumulated production experiences on the R&D competition for the next generation product. We assume that each firm's hazard function governing the innovation process depends on its accumulated production experiences and the cumulative flow of R&D expenditures. We further assume that the incumbent and the challengers are heterogeneous. Only the incumbent can enjoy monopoly profit and accumulated knowledge from production experiences, while all participants have to pay a fixed cost at the outset as well as recurrent flow costs when the R&D competition is underway. Besides the probability distribution governing the timing of innovation, the incumbent's production experiences, the monopoly profit from the post-innovation market, the patent reward and the payoff to the loser will all affect each firm's equilibrium strategy in our model. After proving the existence of a unique Nash equilibrium in this differential game (Theorem 1), we demonstrate analytically that the likelihood of persistent leadership increases with production experiences of the incumbent but decreases with the number of challengers (Theorem 2). It confirms the observation that production experiences can play to the advantage of the incumbent such as Intel. It also shows that destructive innovation is more likely to happen with increased market competition, providing an explanation for the OPC industry example mentioned before. However, it is difficult to obtain a closed-form solution of the optimal investment strategies from a set of nonlinear first-order partial differential equations. Numerical simulations are therefore conducted to explore the properties of equilibrium investment strategies. In the absence of production experience (called the benchmark case), we first confirm (in the appendix) that our numerical analyses reach the same conclusions as in Reinganum's (1983) model, when there is only one incumbent and one challenger. Our numerical analyses further indicate that the incumbent invests less than the challenger when we include the influence of production experiences. This difference increases with production experiences since the challengers’ investment rates increase with production experiences while the incumbent's investment rate decreases with production experiences (Result 1). The difference between the challengers’ and the incumbent's investment rates decreases with the value of being a winner and a loser but increases with the expected waiting time of an innovation and the flow of monopoly profits (Result 2). With a large number of challengers, the persistent leadership in the R&D race is still possible if production experience of the incumbent is sufficiently large. Moreover, the likelihood of persistent leadership increases with the present value of being a winner and a loser but decreases with the expected waiting time of R&D innovation and the flow of monopoly profits (Result 3). The difference between the challengers’ and the incumbent's investment rates increases with the number of challengers in the R&D race (Result 4). The paper is organized as follows. The next section contains the model and the existence and uniqueness result (Theorem 1). In Section 3, we present the analytical result of Theorem 2 and other numerical analyses (Results 1–4). The proof of Theorem 1, discussion of our numerical method and confirmation of the benchmark case (in the absence of production experiences) are included in the appendix. Section 4 concludes the paper.

We summarize the similarities and differences among the results of this paper and those of Reinganum, 1983 and Reinganum, 1985 and Malueg and Tsutsui (1997) in Table 1. First, for the influence of production experiences, we extend the theoretical analyses of Reinganum's (1983) and show that the incumbent can keep its persistent leadership even when its optimal investment is less than those of the challengers. The realities of CPU competition mentioned before provided a good example. On the other hand, the persistent leadership is less likely to occur in an industry with low-tech entry barrier and hence with many challengers, as in the OPC industry mentioned before. This has been demonstrated in Theorem 2 and recorded in the last two cells of the last row of Table 1. This result constitutes a part of the new contributions of this paper.