This section recalls basics of $\CID$ formerly defined in~\cite{fgb11:ip}. 

The set of all $k-$strategies 
is furthere denoted as to  $\mathbb{S}_\mathsf{k}$.
First of all, 
the two
following notations are used:
$\llbracket0;N\rrbracket=\{0,1,\hdots,N\}$, 
and $\mathds{B}=\{0,1\}$.

In the sequel $S^{n}$ denotes the $n^{th}$ term of a sequence $S$ and
$V_{i}$ is for the $i^{th}$ component of a vector $V$. 
Let us recall that for $\mathsf{k} \in \mathds{N}^\ast$, 
a $k-$\emph{strategy} %adapter} 
is a sequence which elements belong into $\llbracket 0, \mathsf{k-1} \rrbracket$. The term ``strategy'' will be used instead
of $k-$strategy when the context will easily
allow to recover $k$.

