Kordonis Ioannis, Lagos Athanasios-Rafail, Papavassilopoulos George P
School of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Polytechniou str., 157 80 Athens, Greece.
Department of Electrical Engineering-Systems, University of Southern California, 3740 McClintock Ave, Los Angeles, CA 90089 United States.
Dyn Games Appl. 2022;12(1):214-236. doi: 10.1007/s13235-021-00403-1. Epub 2021 Oct 11.
Individual behaviors play an essential role in the dynamics of transmission of infectious diseases, including COVID-19. This paper studies a dynamic game model that describes the social distancing behaviors during an epidemic, assuming a continuum of players and individual infection dynamics. The evolution of the players' infection states follows a variant of the well-known SIR dynamics. We assume that the players are not sure about their infection state, and thus, they choose their actions based on their individually perceived probabilities of being susceptible, infected, or removed. The cost of each player depends both on her infection state and on the contact with others. We prove the existence of a Nash equilibrium and characterize Nash equilibria using nonlinear complementarity problems. We then exploit some monotonicity properties of the optimal policies to obtain a reduced-order characterization for Nash equilibrium and reduce its computation to the solution of a low-dimensional optimization problem. It turns out that, even in the symmetric case, where all the players have the same parameters, players may have very different behaviors. We finally present some numerical studies that illustrate this interesting phenomenon and investigate the effects of several parameters, including the players' vulnerability, the time horizon, and the maximum allowed actions, on the optimal policies and the players' costs.
个体行为在包括新冠病毒病（COVID - 19）在内的传染病传播动态中起着至关重要的作用。本文研究了一个动态博弈模型，该模型描述了疫情期间的社交距离行为，假设参与者连续且存在个体感染动态。参与者感染状态的演变遵循著名的SIR动态模型的一个变体。我们假设参与者不确定自己的感染状态，因此，他们根据自己对易感、感染或康复的个体感知概率来选择行动。每个参与者的成本既取决于她的感染状态，也取决于与他人的接触。我们证明了纳什均衡的存在性，并使用非线性互补问题对纳什均衡进行了刻画。然后，我们利用最优策略的一些单调性性质来获得纳什均衡的降阶刻画，并将其计算简化为一个低维优化问题的求解。结果表明，即使在所有参与者具有相同参数的对称情况下，参与者的行为也可能非常不同。我们最后给出了一些数值研究，这些研究说明了这一有趣现象，并研究了包括参与者易感性、时间范围和最大允许行动等几个参数对最优策略和参与者成本的影响。
