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\subsection{Mutual Information: definition and properties}  Mutual Information is widely used for instance for registration of medical images as it is depicted in \cite{Pluim_2003}. The main idea is to introduced introduce  a feature space (or a joint probability) of the two trajectories we want to compare and to evaluate the quantity of information shared by the two trajectories based on this feature space. This quantity is calculate calculated  with Mutual Information. In our case the feature space will be the distribution of the couple of joint  positions of 2 two  players' trajectories during awindow of time during a  few minutes. minutes (we will come to that later).  Thus it corresponds to a 4-dimension distribution. The Mutual Infomation of this distribution will be the lynchpin of our similarity measure for trajectories. \subsubsection{Entropy}  Shannon introduced the entropy to be a measure of the quantity of information of the distribution of a random variable.