On the Reswitching and Convergence Properties of Research & Development Rivalry

Under an alternate assumption of the payoff function, we analyze Lee's dynamic game model of R&D rivalry. Both similarities and differences in the equilibrium results of the model are obtained. It is shown that both the reswitching property and the convergence property of R&D rivalry are robust under the alternate assumption. The reswitching property of R&D rivalry states that after gaining a technological edge against a rival, a decision maker stops doing R&D and he will resume doing R&D when his rival succeeds in narrowing the technological gap between the two rivals. The convergence property of R&D rivalry states that when the technology levels of two rivals differ by a wide margin, the one with a lower technology level will be the only one doing R&D to narrow the technological gap between the two rivals. This formalizes the perception of R&D managers that the R&D decision of one firm should depend on the R&D decision of its rivals for competitive reasons. Moreover, when multiple Nash equilibria exist, a different pair of equilibria is obtained under the alternate assumption. Insights to an antitrust puzzle relevant to managers are provided. Finally, this paper provides an explanation of why the market shares of firms in an industry may differ. At stationary states of technologies, asymmetric technologies (market shares) are expected.