Royal Processions: Incentives, Efficiency and Fairness in Two-sided Matching

TL;DR

This paper characterizes all incentive compatible, efficient, and gender-neutral two-sided matching mechanisms, showing they are recursive and involve sequential rounds with specific matching rules, and proves that one-sided mechanisms are limited to sequential dictatorships.

Contribution

It provides a complete classification of group strategy-proof, efficient, and gender-neutral two-sided matching mechanisms, revealing their recursive structure and limitations of one-sided mechanisms.

Findings

All such mechanisms are recursive and operate in rounds.

In one-sided matching, only sequential dictatorships are possible.

No individually rational, group strategy-proof, and efficient mechanisms exist for one-sided matching.

Abstract

We study the set of incentive compatible and efficient two-sided matching mechanisms. We classify all such mechanisms under an additional assumption -- "gender-neutrality" -- which guarantees that the two sides be treated symmetrically. All group strategy-proof, efficient and gender-neutral mechanisms are recursive and the outcome is decided in a sequence of rounds. In each round, two agents are selected, one from each side. These agents are either "matched-by-default" or "unmatched-by-default." In the former case either of the selected agents can unilaterally force the other to match with them while in the latter case they may only match together if both agree. In either case, if this pair of agents is not matched together, each gets their top choice among the set of remaining agents. As an important step in the characterization, we first show that in one-sided matching all group strategy-proof and efficient mechanisms are sequential dictatorships. An immediate corollary is that there are no individually rational, group strategy-proof and efficient one-sided matching mechanisms.