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).

翻译：网络中关键影响者的选择需防范策略性操纵，这一问题吸引了众多研究者的关注，并具有广泛的实际应用价值。本文旨在根据后代影响力（即影响能力）选择一至两位关键影响者，同时防止智能体操纵其边关系（即激励相容性）。现有研究主要聚焦于单一影响者选择问题。Zhang等人[2021]研究了单智能体选择问题，并证明了该选择问题的最优近似比上界为1/(1+ln2)。本文首先设计了一种可达此上界的机制，进而将该问题拓展至两位智能体选择场景，提出了一种近似比达到(3+ln2)/(4(1+ln2))（约0.54）的机制。