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A recent line of work in mechanism design has focused on guaranteeingincentive compatibility for agents without contingent reasoning skills:obviously strategyproof mechanisms guarantee that it is "obvious" for theseimperfectly rational agents to behave honestly, whereas non-obviouslymanipulable (NOM) mechanisms take a more optimistic view and ensure that theseagents will only misbehave when it is "obvious" for them to do so. Technically,obviousness requires comparing certain extrema (defined over the actions of theother agents) of an agent's utilities for honest behaviour against dishonestbehaviour.  We present a technique for designing NOM mechanisms in settings wheremonetary transfers are allowed based on cycle monotonicity, which allows us todisentangle the specification of the mechanism's allocation from the payments.By leveraging this framework, we completely characterise both allocation andpayment functions of NOM mechanisms for single-parameter agents. We then lookat the classical setting of bilateral trade and study whether and how muchsubsidy is needed to guarantee NOM, efficiency, and individual rationality. Weprove a stark dichotomy; no finite subsidy suffices if agents look only atbest-case extremes, whereas no subsidy at all is required when agents focus onworst-case extremes. We conclude the paper by characterising the NOM mechanismsthat require no subsidies whilst satisfying individual rationality.

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