On the Decentralized Implementation of Lockdown Policies

This paper presents a stylised social-interaction game where the implementation of a lockdown policy is delegated to the decentralised, uncoordinated decision-making of a large population of atomistic agents – assumed risk-neutral and demographically heterogeneous. Compliance with policy prescriptions is socially beneficial but individually costly. In the static, it determines the individual risk of contagion in social interactions (at the micro-level) and the number of new infections (at the macro-). Over time, it affects the peak prevalence of the disease and the duration of the epidemic. Albeit atomistic, agents act strategically, for they rationally anticipate others’ behaviour when deciding (not) to comply. Three are the key results of our analysis. First, the strategic incentives faced by the agents co-evolve with the epidemic. When prevalence is low, compliance is a dominated strategy. When prevalence is high, individual decisions to comply are strategic substitutes: older/weaker agents self-protect by implementing social distancing and younger/healthier ones free-ride. Second, the strategic incentives faced by the agents co-evolve, too, with their beliefs about susceptibility. When they disregard any information about their past behaviour and use the aggregates to estimate susceptibility, strategic substitutability prevails. When beliefs are path-dependent, both complementarity and substitutability may arise. Third, we show that SIR-based models that fail to account for the endogenous response to policy prescriptions may substantially overestimate the effectiveness of lockdowns. Incidentally, we highlight that myopic behaviour may cease to be rational in a dynamic setting where agents’ beliefs about susceptibility are path-dependent.