We study mechanism design when agents may have hidden secondary goals which will manifest as non-trivial preferences among outcomes for which their primary utility is the same. We show that in such cases, a mechanism is robust against strategic manipulation if and only if it is not only incentive-compatible, but also nonbossy -- a well-studied property in the context of matching and allocation mechanisms. We give complete characterizations of incentive-compatible and nonbossy mechanisms in various settings, including auctions with single-parameter agents and public decision settings where all agents share a common outcome. In particular, we show that in the single-item setting, a mechanism is incentive-compatible, individually rational, and nonbossy if and only if it is a sequential posted-price mechanism. In contrast, we show that in more general single-parameter environments, there exist mechanisms satisfying our characterization that significantly outperform sequential posted-price mechanisms in terms of revenue or efficiency (sometimes by an exponential factor).

翻译：我们研究当智能体可能具有隐藏的次要目标——这些目标将表现为在主要效用相同的结局中的非平凡偏好——时的机制设计问题。我们证明，在这种情况下，一个机制对策略操纵具有稳健性当且仅当它不仅满足激励相容性，还满足非支配性——这是匹配与分配机制中一个被广泛研究的性质。我们给出了多种环境下激励相容且非支配性机制的完整刻画，包括单参数智能体的拍卖场景以及所有智能体共享共同结局的公共决策场景。特别地，我们证明在单物品场景中，一个机制满足激励相容性、个体理性及非支配性当且仅当它是一个序贯议价机制。相比之下，我们证明在更一般的单参数环境中，存在满足我们刻画性质的机制，其在收益或效率上显著优于序贯议价机制（有时呈指数级提升）。