Distributed Prediction-Correction Algorithms for Time-Varying Nash Equilibrium Tracking

The candidate reproduces the paper’s Theorem 1 bound ||x_k - x*(t_k)|| ≤ C1 γ^k + C2 h^2 under the same hypotheses, using the same two-phase recursion (k<q and k≥q), the same choices of A,B,D, the same feasibility condition ρ^τ((q+1)/(qγ) + 1/(qγ^{q+1})) ≤ 1, and the same closed-form C2 = c2 √N q(q+1) ρ^τ / (2q - 2ρ^τ(q+2)) as in the paper’s statement and proof. The only minor discrepancy is that the model includes an unnecessary h^2 term in the k<q initialization, but it does not affect correctness. Importantly, the paper contains a conceptual slip in writing ẋ*(t) = F^t(x*(t)) when F^t(x*(t))=0 by definition of NE; however, the key O(h^2) predictor error bound can be justified directly from Assumption 1 (bounded ẍ*(t)), so the main result remains correct. Overall: same argument structure and result; paper needs a small fix in the motivation of Lemma 2. See Theorem 1 with (14)–(16) and Lemmas 2–3 in the paper, and the induction step (18) for the recursion closure .