as shown in (1). In particular, the KL divergence of ${\bf q}\left(\mathcal{X}\right)$ from ${\bf p}\left(\mathcal{X}\right)$ is equal to the difference between the amount of information possessed jointly by the agents, and the corresponding amount of information possessed by the same agents if such information has no redundancies. Throughout the paper, we use $H(X_{-i})$ to denote $H(\mathcal{X}/\{X_{i}\})$, and $\mbox{KL}(\mathcal{X}) = D\left({\bf p}||{\bf q}\right)$ to denote the KL divergence.

Network formation game
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Agents benefit from gathering information by linking to other agents. The link formation strategy adopted by agent $i$ is denoted by a tuple ${\bf g}_{i}=(g_{ij})_{j\in\{1,...,N\}/\{i\}}\in\{0,1\}^{N-1}$; $g_{ij}$ = 1 if agent $i$ forms a link with agent $j$ and $g_{ij}$ = 0 otherwise. We assume unilateral link formation where an agent decides to form a link and solely bears the cost of link formation[^2]. A strategy profile ${\bf g}$ is defined as the collection of strategies of all agents, i.e. ${\bf g}{\vcentcolon=}({\bf g}_{i})_{i=1}^{N}\in{\bf G}$, where ${\bf G}$ is a finite space. When agent $i$ forms a link with agent $j$, it incurs a cost of $c_{ij}$. We define the topology of the network as $\mathcal{T}=\{(i,j)\in\mathcal{N}\times\mathcal{N}|\max\{g_{ij},g_{ji}\}=1\}$. All connected agents exchange information bilaterally; thus $\mathcal{T}$ is an undirected graph. Information is shared 