In this work, we study the additively separable Group Activity Selection Problem (AS-GASP) in an imperfect information setting, where agents have private preferences over activities and weights over other agents. Our goal is to design mechanisms that assign agents to activities based on their declared preferences and weights, with the objective of maximizing social welfare while ensuring truthful reporting. We, therefore, focus on the notion of non-obvious manipulability (NOM), a form of resilience to manipulation. We first investigate the relationship between NOM and social welfare optimality. In this regard, our main result shows that, when preferences and weights are arbitrary or non-negative, any optimal mechanism is non-obviously manipulable. In contrast, when either preferences or weights are binary, we show that optimality and NOM may be incompatible. We then turn to computational aspects. While it is known that computing an optimal outcome for the AS-GASP is NP-hard even in restricted settings, we establish a strong inapproximability result showing that no polynomial-time algorithm can guarantee a bounded approximation ratio when preferences and weights may take arbitrary values. In turn, when preferences are non-negative, we show that a bounded approximation is possible, and we present two asymptotically optimal approximation mechanisms that are also guaranteed to satisfy NOM.

翻译：本文研究了不完全信息环境下的可加可分离群体活动选择问题（AS-GASP），其中智能体对活动拥有私有偏好，并对其他智能体拥有私有权重。我们的目标是设计基于智能体申报的偏好与权重进行活动分配的机制，旨在最大化社会福利的同时确保真实报告。因此，我们聚焦于非明显可操纵性（NOM）这一概念，它是对操纵行为的一种抵御形式。我们首先研究了NOM与社会福利最优性之间的关系。在这方面，我们的主要结果表明：当偏好与权重为任意值或非负值时，任何最优机制都是非明显可操纵的。相反，当偏好或权重为二元值时，我们证明了最优性与NOM可能互不兼容。随后我们转向计算层面的研究。尽管已知即使在受限设定下计算AS-GASP的最优结果也是NP难的，但我们建立了一个强不可近似性结论：当偏好与权重可取任意值时，没有多项式时间算法能够保证有界的近似比。另一方面，当偏好为非负值时，我们证明了有界近似是可行的，并给出了两种渐近最优且保证满足NOM的近似机制。