One of the key features of our economies consists of the coexistence of different technologies supplying similar products and services. We often observe that an old technology is improved when a new one appears; behind this process of improvement often lies an intentional research activity. There thus begins a competition between the two technologies whose performances are improved via R&D. We focus our attention on this competition process and supply a formal model, based on the optimization of R&D expenditure of both technologies, which can describe the dynamics of the delayed overtaking of the new technology over the old one
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