Nonbossy mechanisms: Mechanism design robust to secondary goals

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.