  We show some estimations for the Coffee Shop Problem with a modification
respect the original statement: there is a rival competing against us. We
present different results based on how fast the rival is able to grow. As main
tool, we use a variation of the Wasserstein distance (the Signed Wasserstein
Distance presented by Piccoli, Rossi and Tournus in "A Wasserstein norm for
signed measures, with application to non local transport equation with source
term"), that allow us to work with finite signed measures and fits our problem.
We are able to obtain similar inequalities with this distance to the ones
produced by the canonical Wasserstein distance.
