In this paper, we investigate game-theoretic strategies for containing spreading processes on large-scale networks. Specifically, we consider the class of networked susceptible-infected-susceptible (SIS) epidemics where a large population of agents strategically choose whether to adopt partially effective protection. We define the utilities of the agents which depends on the degree of the agent, its individual infection status and action, as well as the the overall prevalence of the epidemic and strategy profile of the entire population. We further present the coupled dynamics of epidemic evolution as well as strategy update which is assumed to follow the replicator dynamics. By relying on timescale separation arguments, we first derive the optimal strategy of protection adoption by the agents for a given epidemic state, and then present the reduced epidemic dynamics. The existence and uniqueness of endemic equilibrium is rigorously characterized and forms the main result of this paper. Finally, we present extensive numerical results to highlight the impacts of heterogeneous node degrees, infection rates, cost of protection adoption, and effectiveness of protection on the epidemic prevalence at the equilibrium.

翻译：本文研究大规模网络中传播过程的博弈论抑制策略。具体而言，我们考虑网络化易感-感染-易感（SIS）流行病模型，其中大量智能体基于策略选择是否采纳部分有效的防护措施。我们定义了智能体的效用函数，该函数取决于智能体的节点度、个体感染状态与行为选择，以及流行病的整体传播程度和全体人群的策略分布。进一步地，我们建立了流行病演化与策略更新的耦合动力学模型，其中策略更新遵循复制动力学机制。基于时间尺度分离原理，我们首先推导给定流行病状态下智能体采纳防护的最优策略，继而给出约化后的流行病动力学方程。本文严格刻画了地方病平衡点的存在性与唯一性，并以此作为主要理论结果。最后，我们通过大量数值模拟，重点分析了节点度异质性、感染率、防护采纳成本及防护措施有效性对平衡状态下流行病传播程度的影响。