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During epidemics people reduce their social and economic activity to lowertheir risk of infection. Such social distancing strategies will depend oninformation about the course of the epidemic but also on when they expect theepidemic to end, for instance due to vaccination. Typically it is difficult tomake optimal decisions, because the available information is incomplete anduncertain. Here, we show how optimal decision making depends on knowledge aboutvaccination timing in a differential game in which individual decision makinggives rise to Nash equilibria, and the arrival of the vaccine is described by aprobability distribution. We show that the earlier the vaccination is expectedto happen and the more precisely the timing of the vaccination is known, thestronger is the incentive to socially distance. In particular, equilibriumsocial distancing only meaningfully deviates from the no-vaccinationequilibrium course if the vaccine is expected to arrive before the epidemicwould have run its course. We demonstrate how the probability distribution ofthe vaccination time acts as a generalised form of discounting, with thespecial case of an exponential vaccination time distribution directlycorresponding to regular exponential discounting.

Rational social distancing in epidemics with uncertain vaccination timing