Who vaccinates when others matter? Social-circle mediated altruism in a heterogeneous vaccination game

We develop a population game with heterogeneous infection-loss types and social-circle mediated prosociality, where altruists internalize expected infection losses within a setting-specific circle. Equilibrium admits closed-form cutoff rules and an aggregate non-vaccination rate that reduces to two composites: a private-cost pressure ratio and an altruistic-concern index combining altruist prevalence with circle structure. A utilitarian planner yields a socially optimal cutoff; we characterize when circle-mediated altruism is welfare-improving versus welfare-excessive, implying under- or over-vaccination. We embed subsidies, prosocial pledges, and indirect pressure as primitives and obtain closed-form comparative statics and interaction effects: pledges are marginal substitutes for subsidies and pressure, while subsidies and pressure are marginal complements. Policy leverage is greatest in high-contact, high-vulnerability settings, where calibrated norm-based interventions with modest transfers can dominate stringent pressure or large subsidies.