Dynamical Systems Theory compared to Game Theory: The case of the Salamis’s battle

The paper’s map (Eq. 1) and baseline parameters are clearly specified, and its numerical fixed points and Jacobian classifications at G = 0.4, 0.64, and 0.7 match the candidate’s results: baseline E1 is a center and E2 a saddle; for G = 0.64 and 0.7 both equilibria are saddles, with y* > x* as reported in the paper . The paper asserts a “critical value” near 0.64 from diagrams , while the model derives it exactly as G_c = 51/80 ≈ 0.6375 by solving x* = y*, which is consistent with the paper’s narrative. The only caveat is that the paper equates fixed points with Nash equilibria without a formal bridge; still, the dynamical claims checked here are correct. Hence both are correct; the model provides a sharper analytic threshold.