[@Gertz2002]. Furthermore, sorting out the recommendation puzzle – deciding what to suggest to whom – can allow platforms to implement incisive forms of price discrimination[^5].

One of the most effective ways to find out which item should be offered in relation to the user’s needs is grounded on algorithms trained to group or classify together similar objects or similar individuals via collaborative filtering. The goal of algorithms used by platforms, is essentially to lead the decisions made by users, suggesting them a certain good instead of another[^6] in relation to their price sensitivity.

Clustering and classification algorithms (such as those used by CF, like $k$-Means Clustering and $k$-Nearest Neighbours algorithm, $k$-NN[^7]) show though several limitations. As a matter of fact, even if their computational complexity is known to be polynomial in the size of the number of points, such algorithms suffer from major unsolved problems [@xu2005survey; @firdaus2015survey]. These latter are mainly related to sparsity of data, high redundancy, inherent noise, sensitivity to the outliers, clusters dimensional heterogeneity; furthermore, there is no metric to assess the quality of the results [@sarwar2001item; @nguyen2007improving]. In addition to the aforementioned scalabilty and spartisy, recommendation system suffer from the so-called “cold-start" problem [@nguyen2007improving; @castillejo2012social; @konstas2009social; 