Maintaining game-theoretic betweenness centralities in highly dynamic networks is challenging due to the high computational cost of recalculating it from scratch. This paper presents distributed incremental algorithms in the classic CONGEST model for maintaining Shapley- and semi-value-based betweenness centralities. By addressing the challenges of parallel traversal congestion and communication overhead, we propose incremental algorithms with round complexities of \(O(D^G( \mathcal {A}^{max}_\mathcal {B}+\) \(\mathcal {D}^{max}_ \mathcal {B})+ |F_{Batch}|+ |\text {Batch}|)\) for multi-edge updates. Here, \( D^G \) , \( \mathcal {A}^{\max }_{\mathcal {B}} \) and \( \mathcal {D}^{\max }_{\mathcal {B}} \) denote the diameter of the graph, the maximum number of articulation points, and the maximum diameter of the biconnected components, respectively. \( |F_{\text {Batch}}| \) and \(|\text {Batch}|\) represent the number of affected vertices resulting from insertions and the number of inserted edges, respectively. Experimental results demonstrate that the proposed multi-edge incremental algorithm achieves speedup factors of up to \( 7 \times \) and \( 16 \times \) compared to the single-edge incremental algorithm and the static algorithm, respectively.