Co-evolution of Vaccination Behavior and Perceived Vaccination Risk can lead to a Stag-Hunt like Game

The paper derives the same ODE system, fixed points, existence conditions, and stability classification as the candidate solution. In particular: (i) the model equations and piecewise infection risk f(x) are identical to Eq. (7) in the paper, with V(n)=V_L+n(V_H−V_L) and ṅ=n(1−n)[(1+θ)−(2+θ)x] ; (ii) the seven fixed points and their existence conditions are listed exactly as in Appendix B ; (iii) the interior equilibrium exists for (2+θ)C/(C−V_L) < R0 < (2+θ)C/(C−V_H) and is a saddle (det J<0), while boundary equilibria (1) and (2) are stable when R0>(2+θ)C/(C−V_L) and R0<(2+θ)C/(C−V_H), respectively; only corner (5) can be stable, matching the candidate’s Jacobian-based classification and the paper’s case-by-case summary . The paper also states that when R0 lies between the two thresholds, the dynamics is stag-hunt-like with two stable boundary equilibria separated by an interior saddle, in agreement with the candidate’s Part C . Minor typographical sign errors in the paper’s printed formulas for n* and some Jacobian entries do not affect the stated stability classification and regime decomposition; the candidate solution notes and corrects these implicitly by re-deriving the conditions from first principles.