Win-Win Zero-Determinant Strategy to Vaccinate the SIS Network Epidemics

Zero-determinant strategies provide a novel perspective for revealing the relation between a game strategy and the cost, and play an important role in effectively controlling and optimizing the costs against virus spreading in vaccination games. We explore in this paper how the social cost can be optimized when a self-interested individual adopts the newly proposed admin-cost-based zero-determinant strategy (AZDS) to unilaterally control his own cost. In contrast to the traditional belief of the conflicts between personal interest and public (social) interest, we find that the AZDS is a win-win mechanism which presents the advantage in optimizing both the individual cost and social cost simultaneously. Taking into account the differences between the individuals (nodes) in a network, we investigate the topological influence on the performance of the AZDS implemented by the administrator, and conclude that the control capability of the administrator depends on not only one's degree but also the network average degree, and the AZDS implemented by the administrators with different degrees have different sensitivities to the change of economic incentive. Some real social networks with community structure illustrate the effectiveness of the AZDS by introducing the coarse graining method.