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In this paper, 1 propose a game-theoretic, intertemporal model of industrial competition in which active firms innovate, imitate, enter or exit as it is optimal in some prevailing (Markov Perfect) equilibrium. The main novel feature of the approach is that technological change is modelled as advance along a directed graph of technologies. This permits a rigorous formalization of such key notions as technological distance, technological precedence, or switching coss, all of which play a crucial role in the model. In particular, they underlie a process of technological change which is highly path-dependent. The theoretical analysis of the paper centers on existence and ergodicity issues but also investigates the effect of different technological structures (digraphs) on the induced population dynamics.