Controlling a Social Network of Individuals with Coevolving Actions and Opinions

The paper’s Theorem 3 states that Algorithm 1 computes Af in O(n^3), and that ϕ(CX,CY)=1 iff Af=V; moreover the dynamics converges to the equilibrium (x*,y*) obtained by setting x* from Af and solving the linear system for y* (Eq. (9)) . These rely on the best-response form with δi and the controlled setup (Assumptions 1–2) . The candidate solution reproduces the same construction: unique y(x) via an invertible linear system, a monotone set operator whose Kleene iteration matches Algorithm 1, O(n^3) complexity, and the same equilibrium/ϕ characterization. Where the paper argues uniqueness of y(x) using a Friedkin–Johnsen reduction (Lemma 2) , the candidate uses an equivalent M-matrix/spectral-radius argument; and where the paper appeals to monotonicity of the controlled dynamics and its convergence (Theorem 1) , the candidate invokes standard supermodular-game order arguments. No substantive conflict was found; the proofs are essentially the same, with the candidate offering slightly more linear-algebraic detail and lattice-theoretic language.