Achieving Social Optimum in Dynamic Weight Adaptation for Virus Mitigation: A Potential Differential Game Approach

In this paper, a differential game framework is proposed to provide a theoretic underpinning for decentralized mitigation of virus spreading in which each node determines its own control control policy based on local information. To reduce the inefficiency of the Nash equilibrium and allow the decentralized policy to achieve social welfare, we propose a mechanism through a penalty scheme for a class of potential differential games over networks. The differential game under the penalty scheme turns out to be a potential differential game. To investigate the long term behaviors of the weight adaptation scheme, we study their turnpike properties. Numerical experiments are used to corroborate the results and demonstrate how the weight adapts to mitigate virus spreading and turnpike properties of the potential differential game.