We propose a multivariate extension of discrete logistic model to represent the whole competition of m technological products, coming from a technology, in a specific market. The relation to Lotka- Voltera model it is examined and used for an improvement of the model. We apply the proposed model to the data set of the Greek mobile phones market data, consisting of 3 competitors, to evaluate model performance in fitting and forecasting. In both markets the model fitting and forecasting performance is acceptable and encouraging. Finally some remarks, conclusions and future tasks are discussed both methodological and practical about multivariate logistic model.