A Scalable Bayesian Persuasion Framework for Epidemic Containment on Heterogeneous Networks

TL;DR

This paper presents a scalable Bayesian framework for optimizing information disclosure by governments to contain epidemics on heterogeneous networks, accounting for societal structure and individual responses.

Contribution

It introduces a structural decomposition of the government's objectives, simplifying the design of optimal information disclosure policies in complex networked societies.

Findings

Explicit conditions for optimal policies based on risk aversion and prudence.

A structural decomposition separating network effects from utility functions.

Framework applicability to incentive and network design interventions.

Abstract

During an epidemic, the information available to individuals in the society deeply influences their belief of the epidemic spread, and consequently the preventive measures they take to stay safe from the infection. In this paper, we develop a scalable framework for ascertaining the optimal information disclosure a government must make to individuals in a networked society for the purpose of epidemic containment. This problem of information design problem is complicated by the heterogeneous nature of the society, the positive externalities faced by individuals, and the variety in the public response to such disclosures. We use a networked public goods model to capture the underlying societal structure. Our first main result is a structural decomposition of the government's objectives into two independent components -- a component dependent on the utility function of individuals, and another dependent on properties of the underlying network. Since the network dependent term in this decomposition is unaffected by the signals sent by the government, this characterization simplifies the problem of finding the optimal information disclosure policies. We find explicit conditions, in terms of the risk aversion and prudence, under which no disclosure, full disclosure, exaggeration and downplay are the optimal policies. The structural decomposition results are also helpful in studying other forms of interventions like incentive design and network design.