Strategyproofness-Exposing Descriptions of Matching Mechanisms

TL;DR

This paper introduces a new way to describe matching mechanisms through menu descriptions that reveal strategyproofness, providing novel descriptions for DA and TTC mechanisms and proving TTC's strategyproofness in a new way.

Contribution

It offers a novel menu-based description framework for matching mechanisms, including new descriptions for DA and TTC, and demonstrates TTC's strategyproofness through this approach.

Findings

Menu descriptions expose strategyproofness.

New descriptions for DA and TTC mechanisms.

Proof of TTC's strategyproofness using menu descriptions.

Abstract

A menu description exposes strategyproofness by presenting a mechanism to player $i$ in two steps. Step (1) uses others' reports to describe $i$'s menu of potential outcomes. Step (2) uses $i$'s report to select $i$'s favorite outcome from her menu. We provide novel menu descriptions of the Deferred Acceptance (DA) and Top Trading Cycles (TTC) matching mechanisms. For TTC, our description additionally yields a proof of the strategyproofness of TTC's traditional description, in a way that we prove is impossible for DA.