Enabling Imitation-Based Cooperation in Dynamic Social Networks

The paper explicitly states that, once strategies are allowed to change under GM1 partner updates, the only absorbing fixed points are an all‑cooperator complete graph and an all‑defector empty graph, with their stability governed by the chosen strategy‑update rule (BM1/BM2/BM3) . GM1 is defined so that when an ordered pair (i,j) is selected, the undirected edge ij is unilaterally set by the ego i according to the alter j’s strategy, matching the candidate’s operational use of a_ij := s_j for the selected orientation . The candidate provides a clear, self‑contained proof that any absorbing state must be invariant under every possible ordered pair update, which forces strategy unanimity and the corresponding extremal graph; they then check that BM1/BM2/BM3 do not change these two states and that no other state is absorbing. This matches the paper’s claim and fills in details the paper only sketches; minor modeling conventions (e.g., what happens when deg(i)=0 in BM2) should be stated explicitly. Overall, both are correct; the model offers a sharper, explicit proof, while the paper states the result and focuses on simulations and qualitative analysis .