Better with Byzantine: Manipulation-Optimal Mechanisms

A mechanism is manipulable if it is in some agents’ best interest to misrepresent their private information. The

revelation principle

establishes that, roughly, anything that can be accomplished by a manipulable mechanism can also be accomplished with a truthful mechanism. Yet agents often fail to play their optimal manipulations due to computational limitations or various flavors of incompetence and cognitive biases. Thus, manipulable mechanisms in particular should anticipate byzantine play. We study

manipulation-optimal

mechanisms: mechanisms that are undominated by truthful mechanisms when agents act fully rationally, and do better than any truthful mechanism if

any

agent fails to act rationally

in any way

. This enables the mechanism designer to do better than the revelation principle would suggest, and obviates the need to predict byzantine agents’ irrational behavior. We prove a host of possibility and impossibility results for the concept which have the impression of broadly limiting possibility. These results are largely in line with the revelation principle, although the considerations are more subtle and the impossibility not universal.