We study mechanism design when agents may have hidden secondary goals which will play a role when the primary utility of the outcomes is the same. We show that in such cases, a mechanism is immune to strategic manipulation if and only if it is incentive compatible with regard to primary utility -- a property we term "primary incentive compatibility" -- and nonbossy -- a well-studied property in the context of matching and allocation mechanisms. We give complete characterizations of primarily 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 primarily incentive compatible, individually rational, and nonbossy if and only if it is a sequential posted-price mechanism.

翻译：我们研究当代理人可能拥有隐藏的次要目标——这些目标在主效用结果相同时会起作用——时的机制设计。我们证明，在此类情形下，一个机制能够免疫策略性操纵当且仅当该机制关于主效用是激励相容的——我们将此性质称为“主激励相容”——并且是非霸道的——这是匹配与分配机制中一个被广泛研究的性质。我们给出了在多种环境下主激励相容且非霸道机制的完整刻画，包括单参数代理人拍卖以及所有代理人共享共同结果的公共决策场景。特别地，我们证明在单物品场景中，一个机制是主激励相容、个体理性且非霸道的，当且仅当它是一个顺序定价机制。