Nonbossy Mechanisms: Mechanism Design Robust to Secondary Goals
Provides theoretical foundations for mechanism design under secondary goals, relevant to economists and computer scientists designing robust allocation mechanisms.
The paper studies mechanism design when agents have hidden secondary goals that matter only when primary utilities are equal. It shows that robustness to such manipulation requires primary incentive compatibility and nonbossiness, and characterizes such mechanisms in several settings, including proving that in single-item settings they are exactly sequential posted-price mechanisms.
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.