Non-Obvious Manipulability for Single-Parameter Agents and Bilateral Trade

A recent line of work in mechanism design has focused on guaranteeing incentive compatibility for agents without contingent reasoning skills: obviously strategyproof mechanisms guarantee that it is “obvious” for these imperfectly rational agents to behave honestly, whereas non-obviously manipulable (NOM) mechanisms take a more optimistic view and assume that these agents will only misbehave when it is “obvious” for them to do so. Technically, obviousness requires comparing certain extrema (defined over the actions of the other agents) of an agent’s utilities for honest behaviour against dishonest behaviour. We present a technique for designing NOM mechanisms in settings with monetary transfers based on cycle monotonicity, which allows us to disentangle the specification of the mechanism’s allocation from its payments. By leveraging this framework, we completely characterise both allocation and payment functions of NOM mechanisms for single-parameter agents. We then look at the classical setting of bilateral trade and study how much subsidy, if any, is needed to guarantee NOM, efficiency, and individual rationality. We prove a stark dichotomy: no finite subsidy suffices if agents look only at best-case extremes, whereas no subsidy at all is required when agents focus on worst-case extremes.