2404.17082
Evolutionary game dynamics with environmental feedback in a network with two communities
Katherine Betz, Feng Fu, Naoki Masuda
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that, in the symmetric reduction with θ1 = θ12, the 3D system admits a line of interior equilibria L given by x* = 1/(1+θ1) and (1−δ)n1* + δ n12* = [R0 − T0 − P0 θ1 + S0 θ1]/ρ1, and shows L is neutrally stable along itself with the two transverse eigenvalues having negative real parts under the payoff inequality (P0−S0)(R1−T1) > (P1−S1)(R0−T0) (Eq. (19)) and the basic Nash assumptions (Eq. (2)) . The candidate solution derives exactly the same L, linearizes to obtain the same Jacobian structure and characteristic polynomial, identifies the zero eigenvalue tangent to L, and uses the same stability inequality to conclude transverse attraction. Its algebraic identity for J11 matches the paper’s expressions (cf. Appendix E) and the sign analysis is identical in substance . Hence both are correct and essentially the same argument.
Referee report (LaTeX)
\textbf{Recommendation:} no revision \textbf{Journal Tier:} specialist/solid \textbf{Justification:} The audited result—the existence of a neutrally stable line of equilibria in the symmetric case and its transverse stability—is derived correctly and cleanly. The candidate solution reproduces the same manifold and stability conditions via nearly identical linearization and sign analysis, adding an explicit tangent eigenvector without altering the substance. Minor clarifications (feasible segment of the line, explicit positivity of ρ1) would further polish the exposition but are not necessary for correctness.