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

TL;DR

This paper introduces a technique for designing non-obviously manipulable mechanisms for single-parameter agents, characterizes their structure, and analyzes subsidy requirements in bilateral trade to ensure incentive compatibility and individual rationality.

Contribution

It provides a complete characterization of NOM mechanisms for single-parameter agents and analyzes subsidy needs in bilateral trade under different agent perspectives.

Findings

Finite subsidies are insufficient when agents consider best-case scenarios.

No subsidies are needed when agents focus on worst-case scenarios.

NOM mechanisms without subsidies can satisfy individual rationality.

Abstract

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 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.