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

Abstract

A recent line of work in mechanism design has focused on guaranteeing incentive compatibility for agents without contingent reasoning skills: obviously strategyproof mechanisms [20] guarantee that it is "obvious" for these imperfectly rational agents to behave honestly, whereas non-obviously manipulable (NOM) mechanisms [26] take a more optimistic view and ensure 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 where monetary transfers are allowed based on cycle monotonicity, which allows us to disentangle the specification of the mechanism's allocation from the 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 whether and how much subsidy 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. We conclude the paper by characterising the NOM mechanisms that require no subsidies whilst satisfying individual rationality.

Non-Obvious Manipulability of the Rank-Minimizing Mechanism

“…Besides Featherstone (2020), who provides a detailed analysis of rank efficiency criteria and related mechanisms and was discussed in the Introduction, there are only two other papers I am aware of in the economics literature that 6 Following Troyan and Morrill (2020), several other papers have applied non-obvious manipulability to various settings, including Aziz and Lam (2021), Ortega and Segal-Halevi (2019), Archbold et al (2022), and Cerrone et al (2022.…”