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 completely characterize the stationary Nash equilibrium of this setting, 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.

翻译：我们研究了一大批个体在面对易感-感染-易感流行病时，是否选择采用成本高昂但部分有效的防护措施或保持不防护的战略行为。与大多数先前关于流行病博弈的研究不同，我们假设个体在做出决策时并不知晓其真实的感染状态。我们采用贝叶斯说服框架，其中个体接收与其真实感染状态相关的含噪信号，并基于接收信号后感染的后验概率计算期望效用以最大化自身收益。我们完全刻画了这一设定下的平稳纳什均衡，并确定了部分信息披露相较于完全信息披露导致均衡状态下感染个体比例更小的条件，反之亦然。