  Competition between times series often arises in sales prediction, when
similar products are on sale on a marketplace. This article provides a model of
the presence of cannibalization between times series. This model creates a
"competitiveness" function that depends on external features such as price and
margin. It also provides a theoretical guaranty on the error of the model under
some reasonable conditions, and implement this model using a neural network to
compute this competitiveness function. This implementation outperforms other
traditional time series methods and classical neural networks for market share
prediction on a real-world data set.
