Non-Obvious Manipulability of the Rank-Minimizing Mechanism

TL;DR

This paper explores the strategic properties of rank-minimizing mechanisms in assignment problems, showing that mechanisms with full support are non-obviously manipulable, which has implications for their strategic robustness.

Contribution

It demonstrates that rank-minimizing mechanisms with full support are non-obviously manipulable, providing new insights into their strategic behavior and robustness.

Findings

Full support rank-minimizing mechanisms are NOM.

Uniform randomization is NOM.

NOM status depends on the selection rule without full support.

Abstract

In assignment problems, the rank distribution of assigned objects is often used to evaluate match quality. Rank-minimizing (RM) mechanisms directly optimize for average rank. While appealing, a drawback is RM mechanisms are not strategyproof. This paper investigates whether RM satisfies the weaker incentive notion of non-obvious manipulability (NOM, Troyan and Morrill, 2020). I show any RM mechanism with full support - placing positive probability on all rank-minimizing allocations - is NOM. In particular, uniform randomization satisfies this condition. Without full support, whether an RM mechanism is NOM or not depends on the details of the selection rule.