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