Controlling Epidemics: The Value of Information Design

Abstract

During the spread of an infection, agents need to trade off the health costs of getting infected and the economic costs of taking protective actions. An agent’s health cost depends on the action of everyone in the society, leading to a game among agents with strategic substitutes. We study the optimal information disclosure policy of a social planner who observes more information about the status of the infection to maximize the social welfare. We analyze the spread of the infection by developing an extension of the Reed- Frost model on a network. We then characterize the equilibrium of the game among agents, and follow the information design literature to model the social planner’s information disclosure policy as the solution to an optimization problem. Our first result establishes that if the infection transmission rate is sufficiently large or small, it is optimal to fully disclose the information. Conversely, we establish that when the infection transmission rate is not at the extremes, then the optimal policy involves obfuscation. Our second result establishes that full disclosure is optimal when the initial infection probability is sufficiently large. If the initial infection probability is sufficiently small, on the other hand, obfuscation may be optimal, depending on other model parameters. It is not obvious a priori that the optimal information disclosure policy may involve obfuscation only for intermediary transmission rates and small initial infection probabilities

Keywords: Game theory, network formation, contagion process, information design, obfuscation