Dynamic noncooperative R&D in Duopoly with spillovers and technology gap

The purpose of this paper is to show how the dynamics of the technology gap between firms helps demarcate the opposing effects of spillovers on R&D incentives. In this study, we explore the theoretical link between spillovers and technology gap by allowing the rate of spillovers to depend on the latter. In order to demonstrate the relationship between technology gap and R&D incentives, we develop a two stage game of process R&D and output competition for an ex-ante asymmetric duopoly with one-way spillovers. Also the dynamic version of a two stage R&D game is considered and three different (though non-mutually exclusive) sets of results are presented. First, we present a variant of the static AJ model with one-way endogenous spillovers. We show that the existence of a subgame perfect Nash equilibrium (SPNE) requires that the level of spillovers to be low and the initial marginal cost to be high. We show that the relationship between the free-riding behavior of the laggard and the level of spillovers is non-monotonic. We observe that they are positively related as long as the size of spillovers is small. Secondly, we develop a dynamic version of the latter model in a differential game setting. It is shown that if each firm in the industry takes into account the dynamic strategic response of its rival, results can be derived by looking at the transitional dynamics of the firms reaction functions in the neighborhood of the steady state. Lastly, we provide a general framework for analyzing dynamic AJ models with one-way endogenous spillovers. We derive some general conditions that would guarantee the existence of a steady state in a more general class of two stage R&D games with spillovers.