Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bayesian Persuasion for Containing SIS Epidemics with Asymptomatic Infection

Ashish R. Hota, Abhisek Satapathi, Urmee Maitra

TL;DR

This work describes the stationary Nash equilibrium of this setting under suitable assumptions, and identifies conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure.

Abstract

We investigate the strategic behavior of a large population of agents who decide whether to adopt a costly partially effective protection or remain unprotected against the susceptible-infected-susceptible epidemic. In contrast with most prior works on epidemic games, we assume that the agents are not aware of their true infection status while making decisions. We adopt the Bayesian persuasion framework where the agents receive a noisy signal regarding their true infection status, and maximize their expected utility computed using the posterior probability of being infected conditioned on the received signal. We characterize the stationary Nash equilibrium of this setting under suitable assumptions, and identify conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure, and vice versa.

Bayesian Persuasion for Containing SIS Epidemics with Asymptomatic Infection

TL;DR

This work describes the stationary Nash equilibrium of this setting under suitable assumptions, and identifies conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure.

Abstract

We investigate the strategic behavior of a large population of agents who decide whether to adopt a costly partially effective protection or remain unprotected against the susceptible-infected-susceptible epidemic. In contrast with most prior works on epidemic games, we assume that the agents are not aware of their true infection status while making decisions. We adopt the Bayesian persuasion framework where the agents receive a noisy signal regarding their true infection status, and maximize their expected utility computed using the posterior probability of being infected conditioned on the received signal. We characterize the stationary Nash equilibrium of this setting under suitable assumptions, and identify conditions under which partial information disclosure leads to a smaller proportion of infected individuals at the equilibrium compared to full information disclosure, and vice versa.
Paper Structure (11 sections, 3 theorems, 45 equations, 2 figures, 1 table)

This paper contains 11 sections, 3 theorems, 45 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Infection States and Signalling Scheme
  4. Epidemic Evolution under Protection Adoption
  5. Rewards and Utilities
  6. Equilibrium Characterization
  7. Equilibrium under Full Information Disclosure
  8. Equilibrium under Partial Information Disclosure
  9. Discussions
  10. Numerical Results
  11. Conclusion and Future Work

Key Result

Proposition 1

We have the following characterization of SNE when $\mu_{\mathtt{S}} = \mu_{\mathtt{I}} = 1$.

Figures (2)

  • Figure 1: Evolution and convergence of infected proportion, and fraction of population remaining unprotected upon receiving signals $\bar{\mathtt{S}}$ and $\bar{\mathtt{I}}$, to their respective stationary Nash equilibrium values $(y^\star,z^\star_{\bar{\mathtt{S}}},z^\star_{\bar{\mathtt{I}}})$ shown in the title, and (in bottom right panel) comparison of infection level at the stationary Nash equilibrium for different choice of $\mu_{\mathtt{S}}$ and $C_{\mathtt{P}}$.
  • Figure 2: Comparison of infection level at the stationary Nash equilibrium for different choice of $C_{\mathtt{P}}$ when (a) different prior information is used by the agents (left), (b) different values of bounded rationality parameter $\lambda$ (middle), and (c) difference in the infected proportion at the SNE when $\mu_{\mathtt{I}}=1$ and the infected proportion for other values of $\mu_{\mathtt{I}}$. All parameters are in accordance with the table, and $\mu_{\mathtt{S}}=0.8$.

Theorems & Definitions (8)

  • Definition 1
  • Remark 1
  • Proposition 1: Equilibria under FID
  • Proposition 2
  • proof
  • Theorem 1
  • Remark 2
  • proof