The World Health Organization seeks effective ways to alert its member states about global pandemics. Motivated by this challenge, we study a public agency’s problem of designing warning policies to mitigate potential disasters that occur with advance notice. The agency privately receives early information about recurring harmful events and issues warnings to induce an uninformed stakeholder to take preemptive actions. The agency’s decision to issue a warning critically depends on its reputation, which we define as the stake- holder’s belief regarding the accuracy of the agency’s information. The agency faces then a trade-off between eliciting a proper response today and maintaining its reputation in order to elicit responses to future events.
We formulate this problem as a dynamic Bayesian persuasion game, which we solve in closed form. We find that the agency sometimes strategically misrepresents its advance information about a current threat in order to cultivate its future reputation. When its reputation is sufficiently low, the agency downplays the risk and actually downplays more as its reputation improves. By contrast, when its reputation is high, the agency sometimes exaggerates the threat and exaggerates more as its reputation deteriorates. Only when its reputation is moderate does the agency send warning messages that fully disclose its private information.
Our study suggests a plausible and novel rationale for some of the false alarms or omissions observed in practice. We further test the robustness of our findings to imperfect advance information, disasters without advance notice, and heterogeneous receivers.

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