Competition Modelling in Multi-Innovation Diffusions: Multivariate Cellular Automata and Differential Approaches

We introduce a deterministic one\u2013dimensional Cellular Automata model, CA, following Boccara (2004) and extend it to a suitable bivariate probabilistic version where an agent may select, at time t, at most one between two competing innovations. This bivariate automaton is then simplified under a \u201cmean-field approximation\u201d, obtaining a continuous representation that gives rise to the Guseo\u2013Bonaldo synchronic duopolistic model, GB\u2013M (see Bonaldo (1991)). Moreover, we study some characterizations of the more complex two\u2013fold diachronic case