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Selecting influentials in networks against strategic manipulations hasattracted many researchers' attention and it also has many practicalapplications. Here, we aim to select one or two influentials in terms ofprogeny (the influential power) and prevent agents from manipulating theiredges (incentive compatibility). The existing studies mostly focused onselecting a single influential for this setting. Zhang et al. [2021] studiedthe problem of selecting one agent and proved an upper bound of 1/(1+ln2) toapproximate the optimal selection. In this paper, we first design a mechanismto actually reach the bound. Then, we move this forward to choosing two agentsand propose a mechanism to achieve an approximation ratio of (3+ln2)/(4(1+ln2))(approx. 0.54).

Incentive-Compatible Selection for One or Two Influentials