论文标题
NASH社交遥远的游戏具有公平限制：不平等厌恶如何影响流行病的传播
Nash Social Distancing Games with Equity Constraints: How Inequality Aversion Affects the Spread of Epidemics
论文作者
论文摘要
在本文中，我们提出了一个游戏理论模型，描述了流行病的传播期间自愿社会疏远。代理商的回报取决于他们实践的社会疏远以及被感染的可能性。我们考虑两种类型的代理商，即如果被感染的不可算力的代理商，他们的成本很小，而脆弱的代理商的成本更高。对于流行病爆发的建模，我们考虑了涉及易感性，感染和去除的人群的SIR（易感性感染）模型的变体。研究了这个社会疏远游戏的纳什平衡。这项工作的主要贡献是对希望达到较低社会不平等的玩家对收益差异的构成的分析。在这种情况下，我们介绍并描述了具有连续玩家的游戏的广义纳什均衡（GNE）概念。通过数值研究，我们表明不平等限制会导致流行病的传播较慢，并改善了弱势参与者的成本。此外，不平等限制也可能对不可挖掘的玩家有益。
In this paper, we present a game-theoretic model describing voluntary social distancing during the spread of an epidemic. The payoffs of the agents depend on the social distancing they practice and on the probability of getting infected. We consider two types of agents, the non-vulnerable agents who have a small cost if they get infected, and the vulnerable agents who have a higher cost. For the modeling of the epidemic outbreak, we consider a variant of the SIR (Susceptible-Infected-Removed) model involving populations of susceptible, infected, and removed persons of vulnerable and non-vulnerable types. The Nash equilibria of this social distancing game are studied. The main contribution of this work is the analysis of the case where the players, desiring to achieve a low social inequality, pose a bound on the variance of the payoffs. In this case, we introduce and characterize a notion of Generalized Nash Equilibrium (GNE) for games with a continuum of players. Through numerical studies, we show that inequality constraints result in a slower spread of the epidemic and an improved cost for the vulnerable players. Furthermore, it is possible that inequality constraints are beneficial for non-vulnerable players as well.
