The Internet has witnessed an incredible growth in its pervasive use and brought unprecedented convenience to its users. However, an increasing amount of unwanted traffic, such as spam and malware, severely burdens both users and Internet service providers (ISPs), which arouses wide public concern. A Global Trust Management (GTM) system was proposed and demonstrated to be accurate, robust and effective on unwanted traffic control in our previous work (Yan et al., 2011, 2013). But its acceptance by network entities (ISPs and hosts) is crucial to its practical deployment and final success. In this paper, we investigate the acceptance conditions of the GTM system using game theory. Considering the selfish nature of network entities, we address our problem as a social dilemma. To enhance cooperation among network entities, a public-goods-based GTM game is formulated with a trust-based punishment mechanism that can provide the incentives of behaving cooperatively for network entities. Meanwhile, the conditions of the adoption of GTM system are figured out. We also carry out a number of simulations to illustrate the acceptance conditions of the GTM system in practical deployment, and show the effectiveness of the trust-based punishment mechanism. Furthermore, suggestions for ISPs cooperating with antivirus vendors are put forward.