from the total information it possesses minus the linking cost. The formation of links is costly; thus, an agent has to trade off the benefits of the information it obtains from another agent versus the cost it needs to pay for connecting with that agent. The amount of information in $X_{i}$ is quantified by the *entropy* function $H(X_{i})$. In addition, the random variables of all agents may be correlated, which indicates that some agents may possess similar information that is redundant to that of the other agents. The common information between agent $i$ and $j$ is captured by the *mutual information* $I(X_{i};X_{j})$.

The information possessed by the set of agents $\mathcal{N}$ is captured by an *entropic vector* that we define as follows.

**Entropic vector-** a vector $\overrightarrow{{\bf H}}$ is said to be an entropic vector of order $N$ if there exists a random variable tuple $(X_{1},X_{2},...,X_{N})$, where associated with any subset $\mathcal{V}$ of $\mathcal{N}$, there is a joint entropy $H(X_{\mathcal{V}})$ that is an element of $\overrightarrow{{\bf H}}$, where $X_{\mathcal{V}}=\{X_{i}|i\in\mathcal{V}\}$ [@ref20].

The elements of $\overrightarrow{{\bf H}}$ represent the joint entropies between all possible subsets of random variables possessed by agents in $\mathcal{N}$. The set of all entropic vector constitute the *entropic 