Epidemic game theory's default result is tragedy. Rational individuals under-vaccinate because each benefits from others' immunity without bearing the cost themselves. The Nash equilibrium involves less vaccination than the social optimum. Public health requires coercion or incentives to close the gap between selfish and cooperative behavior.
Under conventional SI dynamics with social distancing as the control variable (arXiv:2603.12107), the opposite holds. The unique Nash equilibrium is a bang-bang strategy — do nothing until a threshold, then lock down completely — and this strategy coincides with the socially optimal policy. Individual rationality and collective welfare align without intervention.
The mechanism is the cost structure of social distancing under SI dynamics. Distancing has both a direct cost (economic, social) and an epidemiological benefit (reduced transmission). Under SI dynamics without recovery, once infected you stay infected — the cost of acquiring infection is permanent. This permanence makes rational agents conservative in exactly the way the social planner would want. The individual's selfish calculation — avoid permanent infection — produces the same strategy as the social planner's collective calculation — minimize total infection cost.
The alignment breaks under SIR dynamics (with recovery), where rational agents correctly compute that infection is temporary and recoverable, making them willing to take more risk than the social optimum allows. The permanence of SI infection is what drives the convergence.
The general pattern: when individual stakes are high enough, Nash equilibria converge to social optima. Tragedy of the commons requires that individual consequences be small relative to collective consequences. When individual consequences are large — when infection is permanent, when the resource is non-renewable, when the loss is irreversible — selfishness and cooperation produce the same behavior. The gap between them is a function of the stakes, not a universal feature of game theory.