Non-obvious manipulability in extensive-form mechanisms: the revelation principle for single-parameter agents

Recent work in algorithmic mechanism design focuses on designing mechanisms for agents with bounded rationality , modifying the constraints required to achieve incentive compatibility. Starting with Li's strengthening of strategyproofness, obvious strategyproofness (OSP) requires truthtelling to be "obvious" over dishonesty, roughly meaning that the worst outcome from truthful actions must be no worse than the best outcome for dishonest ones. A celebrated result for dominant-strategy incentive-compatible mechanisms that allows us to restrict attention to direct mechanisms, known as the revelation principle , does not hold for OSP: the implementation details matter for the obvious incentive properties of the mechanism. Studying agent strategies in real-life mechanisms, Troyan and Morrill introduce a relaxation of strategy-proofness known as non-obvious manipulability, which only requires comparing certain extrema of the agents' utility functions in order for a mechanism to be incentive-compatible: a mechanism is not obviously manipulable (NOM) if the best and worst outcomes when acting truthfully are no worse than the best and worst outcomes when acting dishonestly. In this work we first extend the cycle monotonicity framework for direct-revelation NOM mechanism design to indirect mechanisms. We then apply this to two settings, single-parameter agents and mechanisms for two agents in which one has a two-type domain, and show that here the revelation principle holds: direct mechanisms are just as powerful as indirect ones.